diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 406d1ad48..2a775b4bd 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -49,6 +49,7 @@ from pandas._typing import (
     Label,
     Level,
     NaPosition,
+    SequenceNotStr,
     TimedeltaDtypeArg,
     TimestampDtypeArg,
     np_ndarray_anyint,
@@ -288,9 +289,9 @@ class Index(IndexOpsMixin[S1]):
     @name.setter
     def name(self, value) -> None: ...
     @property
-    def names(self) -> list[_str]: ...
+    def names(self) -> list[_str | None]: ...
     @names.setter
-    def names(self, names: list[_str]): ...
+    def names(self, names: SequenceNotStr[_str | None]): ...
     def set_names(self, names, *, level=..., inplace: bool = ...): ...
     @overload
     def rename(self, name, inplace: Literal[False] = False) -> Self: ...
diff --git a/tests/test_indexes.py b/tests/test_indexes.py
index 75c9fc118..b43c21333 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -81,11 +81,17 @@ def test_column_contains() -> None:
     # https://github.com/microsoft/python-type-stubs/issues/199
     df = pd.DataFrame({"A": [1, 2], "B": ["c", "d"], "E": [3, 4]})
 
-    collist = [column for column in df.columns]
-
-    collist2 = [column for column in df.columns[df.columns.str.contains("A|B")]]
-
-    length = len(df.columns[df.columns.str.contains("A|B")])
+    # check accessing the columns as Scalar
+    check(assert_type([column for column in df.columns], list[str]), list)
+    # check slicing the columns with a Series[bool]
+    check(
+        assert_type(
+            [column for column in df.columns[df.columns.str.contains("A|B")]], list[str]
+        ),
+        list,
+    )
+    # check that generic methods are defined on a slice of an index
+    check(assert_type(len(df.columns[df.columns.str.contains("A|B")]), int), int)
 
 
 def test_column_sequence() -> None:
@@ -1160,3 +1166,22 @@ def test_value_counts() -> None:
         pd.Series,
         float,
     )
+
+
+def test_index_naming() -> None:
+    """
+    Test index names type both for the getter and the setter.
+
+    The names of an index should be settable with a sequence (not str) and names
+    property is a list[str | None] (FrozenList).
+    """
+    df = pd.DataFrame({"a": ["a", "b", "c"], "i": [10, 11, 12]})
+
+    df.index.names = ["idx"]
+    check(assert_type(df.index.names, list[str | None]), list)
+    df.index.names = ("idx2",)
+    check(assert_type(df.index.names, list[str | None]), list)
+    df.index.names = [None]
+    check(assert_type(df.index.names, list[str | None]), list)
+    df.index.names = (None,)
+    check(assert_type(df.index.names, list[str | None]), list)