diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index ab242ece981817..a7f7ce776ab69b 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -250,6 +250,18 @@ is respected in indexing. (:issue:`24076`, :issue:`16785`)
     df['2019-01-01 12:00:00+04:00':'2019-01-01 13:00:00+04:00']
 
 
+.. _whatsnew_0250.api_breaking.MultiIndex._names:
+
+
+``MultiIndex.levels`` do not hold level names any longer
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+A :class:`MultiIndex` previously stored the level names as attributes of each of its
+:attr:`MultiIndex.levels`. From Pandas 0.25, the names are only accessed through
+:attr:`MultiIndex.names` (which was also possible previously). This is done in order to
+make :attr:`MultiIndex.levels` more similar to :attr:`CategoricalIndex.categories`.
+
+
 .. _whatsnew_0250.api_breaking.multi_indexing:
 
 
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index a1989fd62b6ee0..7007560e7db347 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -7797,7 +7797,8 @@ def _count_level(self, level, axis=0, numeric_only=False):
         if isinstance(level, str):
             level = count_axis._get_level_number(level)
 
-        level_index = count_axis.levels[level]
+        level_name = count_axis._names[level]
+        level_index = count_axis.levels[level]._shallow_copy(name=level_name)
         level_codes = ensure_int64(count_axis.codes[level])
         counts = lib.count_level_2d(mask, level_codes, len(level_index), axis=0)
 
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 71b551adaf3ef1..ee772514f678c4 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -259,6 +259,7 @@ def __new__(
         result._set_levels(levels, copy=copy, validate=False)
         result._set_codes(codes, copy=copy, validate=False)
 
+        result._names = [None for _ in levels]
         if names is not None:
             # handles name validation
             result._set_names(names)
@@ -1176,7 +1177,7 @@ def __len__(self):
         return len(self.codes[0])
 
     def _get_names(self):
-        return FrozenList(level.name for level in self.levels)
+        return FrozenList(self._names)
 
     def _set_names(self, names, level=None, validate=True):
         """
@@ -1222,7 +1223,7 @@ def _set_names(self, names, level=None, validate=True):
             level = [self._get_level_number(l) for l in level]
 
         # set the name
-        for l, name in zip(level, names):
+        for lev, name in zip(level, names):
             if name is not None:
                 # GH 20527
                 # All items in 'names' need to be hashable:
@@ -1232,7 +1233,7 @@ def _set_names(self, names, level=None, validate=True):
                             self.__class__.__name__
                         )
                     )
-            self.levels[l].rename(name, inplace=True)
+            self._names[lev] = name
 
     names = property(
         fset=_set_names, fget=_get_names, doc="""\nNames of levels in MultiIndex\n"""
@@ -1546,13 +1547,13 @@ def _get_level_values(self, level, unique=False):
         values : ndarray
         """
 
-        values = self.levels[level]
+        lev = self.levels[level]
         level_codes = self.codes[level]
+        name = self._names[level]
         if unique:
             level_codes = algos.unique(level_codes)
-        filled = algos.take_1d(values._values, level_codes, fill_value=values._na_value)
-        values = values._shallow_copy(filled)
-        return values
+        filled = algos.take_1d(lev._values, level_codes, fill_value=lev._na_value)
+        return lev._shallow_copy(filled, name=name)
 
     def get_level_values(self, level):
         """
diff --git a/pandas/core/reshape/reshape.py b/pandas/core/reshape/reshape.py
index 5d932d7ded9b8c..9f6155822bee1c 100644
--- a/pandas/core/reshape/reshape.py
+++ b/pandas/core/reshape/reshape.py
@@ -260,10 +260,13 @@ def get_new_values(self):
     def get_new_columns(self):
         if self.value_columns is None:
             if self.lift == 0:
-                return self.removed_level
+                lev = self.removed_level._shallow_copy()
+                lev.name = self.removed_name
+                return lev
 
-            lev = self.removed_level
-            return lev.insert(0, lev._na_value)
+            lev = self.removed_level.insert(0, item=self.removed_level._na_value)
+            lev.name = self.removed_name
+            return lev
 
         stride = len(self.removed_level) + self.lift
         width = len(self.value_columns)
@@ -302,7 +305,9 @@ def get_new_index(self):
             lev, lab = self.new_index_levels[0], result_codes[0]
             if (lab == -1).any():
                 lev = lev.insert(len(lev), lev._na_value)
-            return lev.take(lab)
+            new_index = lev.take(lab)
+            new_index.name = self.new_index_names[0]
+            return new_index
 
         return MultiIndex(
             levels=self.new_index_levels,
@@ -658,7 +663,9 @@ def _convert_level_number(level_num, columns):
         new_names = this.columns.names[:-1]
         new_columns = MultiIndex.from_tuples(unique_groups, names=new_names)
     else:
-        new_columns = unique_groups = this.columns.levels[0]
+        new_columns = this.columns.levels[0]._shallow_copy()
+        new_columns.name = this.columns.names[0]
+        unique_groups = new_columns
 
     # time to ravel the values
     new_data = {}
diff --git a/pandas/io/json/table_schema.py b/pandas/io/json/table_schema.py
index 045127c63af5c2..ec417d1d8bfad2 100644
--- a/pandas/io/json/table_schema.py
+++ b/pandas/io/json/table_schema.py
@@ -243,8 +243,10 @@ def build_table_schema(data, index=True, primary_key=None, version=True):
 
     if index:
         if data.index.nlevels > 1:
-            for level in data.index.levels:
-                fields.append(convert_pandas_type_to_json_field(level))
+            for level, name in zip(data.index.levels, data.index.names):
+                new_field = convert_pandas_type_to_json_field(level)
+                new_field["name"] = name
+                fields.append(new_field)
         else:
             fields.append(convert_pandas_type_to_json_field(data.index))
 
diff --git a/pandas/tests/frame/test_alter_axes.py b/pandas/tests/frame/test_alter_axes.py
index 2ce65bd15387ee..869418bee8e155 100644
--- a/pandas/tests/frame/test_alter_axes.py
+++ b/pandas/tests/frame/test_alter_axes.py
@@ -979,7 +979,7 @@ def test_reset_index(self, float_frame):
         ):
             values = lev.take(level_codes)
             name = names[i]
-            tm.assert_index_equal(values, Index(deleveled[name]))
+            tm.assert_index_equal(values, Index(deleveled[name]), check_names=False)
 
         stacked.index.names = [None, None]
         deleveled2 = stacked.reset_index()
diff --git a/pandas/tests/indexes/multi/test_astype.py b/pandas/tests/indexes/multi/test_astype.py
index 4adcdd0112b264..f320a89c471bfb 100644
--- a/pandas/tests/indexes/multi/test_astype.py
+++ b/pandas/tests/indexes/multi/test_astype.py
@@ -11,7 +11,7 @@ def test_astype(idx):
     actual = idx.astype("O")
     assert_copy(actual.levels, expected.levels)
     assert_copy(actual.codes, expected.codes)
-    assert [level.name for level in actual.levels] == list(expected.names)
+    assert actual.names == list(expected.names)
 
     with pytest.raises(TypeError, match="^Setting.*dtype.*object"):
         idx.astype(np.dtype(int))
diff --git a/pandas/tests/indexes/multi/test_constructor.py b/pandas/tests/indexes/multi/test_constructor.py
index 1b6177ede30ec9..20138eb851d89a 100644
--- a/pandas/tests/indexes/multi/test_constructor.py
+++ b/pandas/tests/indexes/multi/test_constructor.py
@@ -17,7 +17,7 @@ def test_constructor_single_level():
         levels=[["foo", "bar", "baz", "qux"]], codes=[[0, 1, 2, 3]], names=["first"]
     )
     assert isinstance(result, MultiIndex)
-    expected = Index(["foo", "bar", "baz", "qux"], name="first")
+    expected = Index(["foo", "bar", "baz", "qux"])
     tm.assert_index_equal(result.levels[0], expected)
     assert result.names == ["first"]
 
@@ -292,8 +292,9 @@ def test_from_arrays_empty():
     # 1 level
     result = MultiIndex.from_arrays(arrays=[[]], names=["A"])
     assert isinstance(result, MultiIndex)
-    expected = Index([], name="A")
+    expected = Index([])
     tm.assert_index_equal(result.levels[0], expected)
+    assert result.names == ["A"]
 
     # N levels
     for N in [2, 3]:
@@ -426,8 +427,9 @@ def test_from_product_empty_zero_levels():
 
 def test_from_product_empty_one_level():
     result = MultiIndex.from_product([[]], names=["A"])
-    expected = pd.Index([], name="A")
+    expected = pd.Index([])
     tm.assert_index_equal(result.levels[0], expected)
+    assert result.names == ["A"]
 
 
 @pytest.mark.parametrize(
diff --git a/pandas/tests/indexes/multi/test_names.py b/pandas/tests/indexes/multi/test_names.py
index 5856cb56b307b8..754e512c5acf30 100644
--- a/pandas/tests/indexes/multi/test_names.py
+++ b/pandas/tests/indexes/multi/test_names.py
@@ -27,28 +27,25 @@ def test_index_name_retained():
 
 
 def test_changing_names(idx):
-
-    # names should be applied to levels
-    level_names = [level.name for level in idx.levels]
-    check_level_names(idx, idx.names)
+    assert [level.name for level in idx.levels] == [None, None]
 
     view = idx.view()
     copy = idx.copy()
     shallow_copy = idx._shallow_copy()
 
-    # changing names should change level names on object
+    # changing names should not change level names on object
     new_names = [name + "a" for name in idx.names]
     idx.names = new_names
-    check_level_names(idx, new_names)
+    check_level_names(idx, [None, None])
 
-    # but not on copies
-    check_level_names(view, level_names)
-    check_level_names(copy, level_names)
-    check_level_names(shallow_copy, level_names)
+    # and not on copies
+    check_level_names(view, [None, None])
+    check_level_names(copy, [None, None])
+    check_level_names(shallow_copy, [None, None])
 
     # and copies shouldn't change original
     shallow_copy.names = [name + "c" for name in shallow_copy.names]
-    check_level_names(idx, new_names)
+    check_level_names(idx, [None, None])
 
 
 def test_take_preserve_name(idx):
@@ -84,7 +81,8 @@ def test_names(idx, index_names):
     # names are assigned in setup
     names = index_names
     level_names = [level.name for level in idx.levels]
-    assert names == level_names
+    assert names == ["first", "second"]
+    assert level_names == [None, None]
 
     # setting bad names on existing
     index = idx
@@ -111,9 +109,8 @@ def test_names(idx, index_names):
 
     # names are assigned
     index.names = ["a", "b"]
-    ind_names = list(index.names)
     level_names = [level.name for level in index.levels]
-    assert ind_names == level_names
+    assert level_names == [None, None]
 
 
 def test_duplicate_level_names_access_raises(idx):
diff --git a/pandas/tests/indexes/multi/test_reindex.py b/pandas/tests/indexes/multi/test_reindex.py
index 88de4d1e803868..1da8b449be4b24 100644
--- a/pandas/tests/indexes/multi/test_reindex.py
+++ b/pandas/tests/indexes/multi/test_reindex.py
@@ -13,12 +13,12 @@ def check_level_names(index, names):
 def test_reindex(idx):
     result, indexer = idx.reindex(list(idx[:4]))
     assert isinstance(result, MultiIndex)
-    check_level_names(result, idx[:4].names)
+    check_level_names(result, [None, None])
 
     result, indexer = idx.reindex(list(idx))
     assert isinstance(result, MultiIndex)
     assert indexer is None
-    check_level_names(result, idx.names)
+    check_level_names(result, [None, None])
 
 
 def test_reindex_level(idx):
diff --git a/pandas/tests/indexes/multi/test_reshape.py b/pandas/tests/indexes/multi/test_reshape.py
index a30e6f33d14998..e79f212f300785 100644
--- a/pandas/tests/indexes/multi/test_reshape.py
+++ b/pandas/tests/indexes/multi/test_reshape.py
@@ -15,10 +15,11 @@ def test_insert(idx):
     # key not contained in all levels
     new_index = idx.insert(0, ("abc", "three"))
 
-    exp0 = Index(list(idx.levels[0]) + ["abc"], name="first")
+    exp0 = Index(list(idx.levels[0]) + ["abc"])
     tm.assert_index_equal(new_index.levels[0], exp0)
+    assert new_index.names == ["first", "second"]
 
-    exp1 = Index(list(idx.levels[1]) + ["three"], name="second")
+    exp1 = Index(list(idx.levels[1]) + ["three"])
     tm.assert_index_equal(new_index.levels[1], exp1)
     assert new_index[0] == ("abc", "three")
 
diff --git a/pandas/tests/reshape/test_concat.py b/pandas/tests/reshape/test_concat.py
index 6366bf0521fbc2..6bb70ef6f6c03c 100644
--- a/pandas/tests/reshape/test_concat.py
+++ b/pandas/tests/reshape/test_concat.py
@@ -1220,8 +1220,10 @@ def test_concat_keys_specific_levels(self):
             names=["group_key"],
         )
 
-        tm.assert_index_equal(result.columns.levels[0], Index(level, name="group_key"))
-        assert result.columns.names[0] == "group_key"
+        tm.assert_index_equal(result.columns.levels[0], Index(level))
+        tm.assert_index_equal(result.columns.levels[1], Index([0, 1, 2, 3]))
+
+        assert result.columns.names == ["group_key", None]
 
     def test_concat_dataframe_keys_bug(self, sort):
         t1 = DataFrame(
@@ -1410,10 +1412,8 @@ def test_concat_keys_and_levels(self):
             keys=[("foo", "one"), ("foo", "two"), ("baz", "one"), ("baz", "two")],
             names=["first", "second"],
         )
-        assert result.index.names == ("first", "second") + (None,)
-        tm.assert_index_equal(
-            result.index.levels[0], Index(["baz", "foo"], name="first")
-        )
+        assert result.index.names == ("first", "second", None)
+        tm.assert_index_equal(result.index.levels[0], Index(["baz", "foo"]))
 
     def test_concat_keys_levels_no_overlap(self):
         # GH #1406
diff --git a/pandas/tests/reshape/test_reshape.py b/pandas/tests/reshape/test_reshape.py
index 1c9e3e57bc310d..7649acd86ab962 100644
--- a/pandas/tests/reshape/test_reshape.py
+++ b/pandas/tests/reshape/test_reshape.py
@@ -617,7 +617,7 @@ def test_reshaping_multi_index_categorical(self):
         df.index.names = ["major", "minor"]
         df["str"] = "foo"
 
-        dti = df.index.levels[0]
+        dti = df.index.levels[0].set_names(["major"])
 
         df["category"] = df["str"].astype("category")
         result = df["category"].unstack()
diff --git a/pandas/tests/test_multilevel.py b/pandas/tests/test_multilevel.py
index a76f2bb04a5420..cd3b09f0f7350a 100644
--- a/pandas/tests/test_multilevel.py
+++ b/pandas/tests/test_multilevel.py
@@ -960,13 +960,11 @@ def test_count(self):
 
         result = series.count(level="b")
         expect = self.series.count(level=1)
-        tm.assert_series_equal(result, expect, check_names=False)
-        assert result.index.name == "b"
+        tm.assert_series_equal(result, expect)
 
         result = series.count(level="a")
         expect = self.series.count(level=0)
-        tm.assert_series_equal(result, expect, check_names=False)
-        assert result.index.name == "a"
+        tm.assert_series_equal(result, expect)
 
         msg = "Level x not found"
         with pytest.raises(KeyError, match=msg):
@@ -1020,10 +1018,10 @@ def aggf(x):
         # for good measure, groupby detail
         level_index = frame._get_axis(axis).levels[level]
 
-        tm.assert_index_equal(leftside._get_axis(axis), level_index)
-        tm.assert_index_equal(rightside._get_axis(axis), level_index)
+        tm.assert_index_equal(leftside._get_axis(axis), level_index, check_names=False)
+        tm.assert_index_equal(rightside._get_axis(axis), level_index, check_names=False)
 
-        tm.assert_frame_equal(leftside, rightside)
+        tm.assert_frame_equal(leftside, rightside, check_names=False)
 
     def test_stat_op_corner(self):
         obj = Series([10.0], index=MultiIndex.from_tuples([(2, 3)]))
@@ -1609,12 +1607,12 @@ def test_constructor_with_tz(self):
         )
 
         result = MultiIndex.from_arrays([index, columns])
-        tm.assert_index_equal(result.levels[0], index)
-        tm.assert_index_equal(result.levels[1], columns)
+        tm.assert_index_equal(result.levels[0], index, check_names=False)
+        tm.assert_index_equal(result.levels[1], columns, check_names=False)
 
         result = MultiIndex.from_arrays([Series(index), Series(columns)])
-        tm.assert_index_equal(result.levels[0], index)
-        tm.assert_index_equal(result.levels[1], columns)
+        tm.assert_index_equal(result.levels[0], index, check_names=False)
+        tm.assert_index_equal(result.levels[1], columns, check_names=False)
 
     def test_set_index_datetime(self):
         # GH 3950
@@ -1642,12 +1640,14 @@ def test_set_index_datetime(self):
         expected = expected.tz_localize("UTC").tz_convert("US/Pacific")
 
         df = df.set_index("label", append=True)
-        tm.assert_index_equal(df.index.levels[0], expected)
-        tm.assert_index_equal(df.index.levels[1], Index(["a", "b"], name="label"))
+        tm.assert_index_equal(df.index.levels[0], expected, check_names=False)
+        tm.assert_index_equal(df.index.levels[1], Index(["a", "b"]))
+        assert df.index.names == ["datetime", "label"]
 
         df = df.swaplevel(0, 1)
-        tm.assert_index_equal(df.index.levels[0], Index(["a", "b"], name="label"))
-        tm.assert_index_equal(df.index.levels[1], expected)
+        tm.assert_index_equal(df.index.levels[0], Index(["a", "b"]))
+        tm.assert_index_equal(df.index.levels[1], expected, check_names=False)
+        assert df.index.names == ["label", "datetime"]
 
         df = DataFrame(np.random.random(6))
         idx1 = pd.DatetimeIndex(