diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index ee772514f678c4..0cd935e64364ee 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -259,7 +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]
+        result._names = [None] * len(levels)
         if names is not None:
             # handles name validation
             result._set_names(names)
diff --git a/pandas/core/reshape/reshape.py b/pandas/core/reshape/reshape.py
index 9f6155822bee1c..4da7e7e58d4b2b 100644
--- a/pandas/core/reshape/reshape.py
+++ b/pandas/core/reshape/reshape.py
@@ -260,13 +260,10 @@ def get_new_values(self):
     def get_new_columns(self):
         if self.value_columns is None:
             if self.lift == 0:
-                lev = self.removed_level._shallow_copy()
-                lev.name = self.removed_name
-                return lev
+                return self.removed_level._shallow_copy(name=self.removed_name)
 
             lev = self.removed_level.insert(0, item=self.removed_level._na_value)
-            lev.name = self.removed_name
-            return lev
+            return lev.rename(self.removed_name)
 
         stride = len(self.removed_level) + self.lift
         width = len(self.value_columns)
@@ -302,12 +299,10 @@ def get_new_index(self):
 
         # construct the new index
         if len(self.new_index_levels) == 1:
-            lev, lab = self.new_index_levels[0], result_codes[0]
-            if (lab == -1).any():
-                lev = lev.insert(len(lev), lev._na_value)
-            new_index = lev.take(lab)
-            new_index.name = self.new_index_names[0]
-            return new_index
+            level, level_codes = self.new_index_levels[0], result_codes[0]
+            if (level_codes == -1).any():
+                level = level.insert(len(level), level._na_value)
+            return level.take(level_codes).rename(self.new_index_names[0])
 
         return MultiIndex(
             levels=self.new_index_levels,
@@ -663,8 +658,7 @@ 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 = this.columns.levels[0]._shallow_copy()
-        new_columns.name = this.columns.names[0]
+        new_columns = this.columns.levels[0]._shallow_copy(name=this.columns.names[0])
         unique_groups = new_columns
 
     # time to ravel the values
diff --git a/pandas/tests/frame/test_alter_axes.py b/pandas/tests/frame/test_alter_axes.py
index 869418bee8e155..3b1b9d1f6be363 100644
--- a/pandas/tests/frame/test_alter_axes.py
+++ b/pandas/tests/frame/test_alter_axes.py
@@ -980,6 +980,7 @@ def test_reset_index(self, float_frame):
             values = lev.take(level_codes)
             name = names[i]
             tm.assert_index_equal(values, Index(deleveled[name]), check_names=False)
+            assert values.name is None
 
         stacked.index.names = [None, None]
         deleveled2 = stacked.reset_index()