diff --git a/pandas-stubs/core/indexes/base.pyi b/pandas-stubs/core/indexes/base.pyi
index 704053c2..0d7b440e 100644
--- a/pandas-stubs/core/indexes/base.pyi
+++ b/pandas-stubs/core/indexes/base.pyi
@@ -58,6 +58,7 @@ from pandas._typing import (
     NaPosition,
     ReindexMethod,
     Scalar,
+    SequenceNotStr,
     SliceType,
     TimedeltaDtypeArg,
     TimestampDtypeArg,
@@ -316,11 +317,11 @@ class Index(IndexOpsMixin[S1]):
     @property
     def name(self) -> Hashable | None: ...
     @name.setter
-    def name(self, value) -> None: ...
+    def name(self, value: Hashable) -> None: ...
     @property
-    def names(self) -> list[Hashable]: ...
+    def names(self) -> list[Hashable | None]: ...
     @names.setter
-    def names(self, names: Sequence[Hashable]) -> None: ...
+    def names(self, names: SequenceNotStr[Hashable | None]) -> 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 e619151b..6286d741 100644
--- a/tests/test_indexes.py
+++ b/tests/test_indexes.py
@@ -1,5 +1,6 @@
 from __future__ import annotations
 
+from collections.abc import Hashable
 import datetime as dt
 from typing import (
     TYPE_CHECKING,
@@ -1433,3 +1434,23 @@ def test_multiindex_range() -> None:
         [range(3), pd.Series([2, 3, 5])],
     )
     check(assert_type(midx_mixed_types, pd.MultiIndex), pd.MultiIndex)
+
+
+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[Hashable | None] (FrozenList).
+    """
+    df = pd.DataFrame({"a": ["a", "b", "c"], "i": [10, 11, 12]})
+
+    df.index.names = ["idx"]
+    check(assert_type(df.index.names, list[Hashable | None]), list)
+    df.index.names = [3]
+    check(assert_type(df.index.names, list[Hashable | None]), list)
+    df.index.names = ("idx2",)
+    check(assert_type(df.index.names, list[Hashable | None]), list)
+    df.index.names = [None]
+    check(assert_type(df.index.names, list[Hashable | None]), list)
+    df.index.names = (None,)
+    check(assert_type(df.index.names, list[Hashable | None]), list)