API: Restore getting name from MultiIndex level

xref https://issues.apache.org/jira/browse/ARROW-6922 /
pandas-dev#27242 (comment)
/ pandas-dev#29032

No docs yet, since it isn't clear how this will eventually sort out. But
we at least want to preserve this behavior for 1.0

pandas/core/indexes/multi.py

@@ -639,7 +639,10 @@ def from_frame(cls, df, sortorder=None, names=None):
 
     @property
     def levels(self):
-        return self._levels
+        result = [
+            x._shallow_copy(name=name) for x, name in zip(self._levels, self._names)
+        ]
+        return FrozenList(result)
 
     @property
     def _values(self):
@@ -830,7 +833,7 @@ def _set_codes(
         if level is None:
             new_codes = FrozenList(
                 _ensure_frozen(level_codes, lev, copy=copy)._shallow_copy()
-                for lev, level_codes in zip(self.levels, codes)
+                for lev, level_codes in zip(self._levels, codes)
             )
         else:
             level = [self._get_level_number(l) for l in level]

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"])
+    expected = Index(["foo", "bar", "baz", "qux"], name="first")
     tm.assert_index_equal(result.levels[0], expected)
     assert result.names == ["first"]
 
@@ -292,7 +292,7 @@ def test_from_arrays_empty():
     # 1 level
     result = MultiIndex.from_arrays(arrays=[[]], names=["A"])
     assert isinstance(result, MultiIndex)
-    expected = Index([])
+    expected = Index([], name="A")
     tm.assert_index_equal(result.levels[0], expected)
     assert result.names == ["A"]
 
@@ -440,7 +440,7 @@ def test_from_product_empty_zero_levels():
 
 def test_from_product_empty_one_level():
     result = MultiIndex.from_product([[]], names=["A"])
-    expected = pd.Index([])
+    expected = pd.Index([], name="A")
     tm.assert_index_equal(result.levels[0], expected)
     assert result.names == ["A"]
 

pandas/tests/indexes/multi/test_names.py

@@ -27,7 +27,7 @@ def test_index_name_retained():
 
 
 def test_changing_names(idx):
-    assert [level.name for level in idx.levels] == [None, None]
+    assert [level.name for level in idx.levels] == ["first", "second"]
 
     view = idx.view()
     copy = idx.copy()
@@ -36,16 +36,16 @@ def test_changing_names(idx):
     # 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, [None, None])
+    check_level_names(idx, ["firsta", "seconda"])
 
     # and not on copies
-    check_level_names(view, [None, None])
-    check_level_names(copy, [None, None])
-    check_level_names(shallow_copy, [None, None])
+    check_level_names(view, ["first", "second"])
+    check_level_names(copy, ["first", "second"])
+    check_level_names(shallow_copy, ["first", "second"])
 
     # and copies shouldn't change original
     shallow_copy.names = [name + "c" for name in shallow_copy.names]
-    check_level_names(idx, [None, None])
+    check_level_names(idx, ["firsta", "seconda"])
 
 
 def test_take_preserve_name(idx):
@@ -81,7 +81,7 @@ def test_names(idx, index_names):
     # names are assigned in setup
     assert index_names == ["first", "second"]
     level_names = [level.name for level in idx.levels]
-    assert level_names == [None, None]
+    assert level_names == index_names
 
     # setting bad names on existing
     index = idx
@@ -109,11 +109,18 @@ def test_names(idx, index_names):
     # names are assigned on index, but not transferred to the levels
     index.names = ["a", "b"]
     level_names = [level.name for level in index.levels]
-    assert level_names == [None, None]
+    assert level_names == ["a", "b"]
 
 
 def test_duplicate_level_names_access_raises(idx):
     # GH19029
     idx.names = ["foo", "foo"]
     with pytest.raises(ValueError, match="name foo occurs multiple times"):
         idx._get_level_number("foo")
+
+
+def test_get_names_from_levels():
+    idx = pd.MultiIndex.from_product([["a"], [1, 2]], names=["a", "b"])
+
+    assert idx.levels[0].name == "a"
+    assert idx.levels[1].name == "b"

pandas/tests/indexes/multi/test_reindex.py

@@ -10,13 +10,13 @@ def test_reindex(idx):
     result, indexer = idx.reindex(list(idx[:4]))
     assert isinstance(result, MultiIndex)
     assert result.names == ["first", "second"]
-    assert [level.name for level in result.levels] == [None, None]
+    assert [level.name for level in result.levels] == ["first", "second"]
 
     result, indexer = idx.reindex(list(idx))
     assert isinstance(result, MultiIndex)
     assert indexer is None
     assert result.names == ["first", "second"]
-    assert [level.name for level in result.levels] == [None, None]
+    assert [level.name for level in result.levels] == ["first", "second"]
 
 
 def test_reindex_level(idx):

pandas/tests/indexes/multi/test_reshape.py

@@ -15,11 +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"])
+    exp0 = Index(list(idx.levels[0]) + ["abc"], name="first")
     tm.assert_index_equal(new_index.levels[0], exp0)
     assert new_index.names == ["first", "second"]
 
-    exp1 = Index(list(idx.levels[1]) + ["three"])
+    exp1 = Index(list(idx.levels[1]) + ["three"], name="second")
     tm.assert_index_equal(new_index.levels[1], exp1)
     assert new_index[0] == ("abc", "three")