diff --git a/src/snowflake/snowpark/modin/plugin/extensions/base_overrides.py b/src/snowflake/snowpark/modin/plugin/extensions/base_overrides.py
index aeca9d6e305..d364c5f57fa 100644
--- a/src/snowflake/snowpark/modin/plugin/extensions/base_overrides.py
+++ b/src/snowflake/snowpark/modin/plugin/extensions/base_overrides.py
@@ -2262,7 +2262,7 @@ def _get_index(self):
         return self._query_compiler.index
 
     idx = Index(query_compiler=self._query_compiler)
-    idx._set_parent(self)
+    idx._parent.set_parent(self)
     return idx
 
 
diff --git a/src/snowflake/snowpark/modin/plugin/extensions/datetime_index.py b/src/snowflake/snowpark/modin/plugin/extensions/datetime_index.py
index 7795d35c746..8f62e6e0dc6 100644
--- a/src/snowflake/snowpark/modin/plugin/extensions/datetime_index.py
+++ b/src/snowflake/snowpark/modin/plugin/extensions/datetime_index.py
@@ -46,7 +46,7 @@
 from snowflake.snowpark.modin.plugin.compiler.snowflake_query_compiler import (
     SnowflakeQueryCompiler,
 )
-from snowflake.snowpark.modin.plugin.extensions.index import Index
+from snowflake.snowpark.modin.plugin.extensions.index import Index, IndexParent
 from snowflake.snowpark.modin.plugin.utils.error_message import (
     datetime_index_not_implemented,
 )
@@ -162,8 +162,7 @@ def __new__(
             query_compiler = query_compiler.series_to_datetime(include_index=True)
         index._query_compiler = query_compiler
         # `_parent` keeps track of any Series or DataFrame that this Index is a part of.
-        index._parent = None
-        index._parent_qc = None
+        index._parent = IndexParent()
         return index
 
     def __init__(
diff --git a/src/snowflake/snowpark/modin/plugin/extensions/index.py b/src/snowflake/snowpark/modin/plugin/extensions/index.py
index 63290803480..a5e541c2229 100644
--- a/src/snowflake/snowpark/modin/plugin/extensions/index.py
+++ b/src/snowflake/snowpark/modin/plugin/extensions/index.py
@@ -71,6 +71,41 @@
 }
 
 
+class IndexParent:
+    def __init__(self) -> None:
+        """
+        Initialize the IndexParent object.
+
+        IndexParent is used to keep track of the parent object that the Index is a part of.
+        It tracks the parent object and the parent object's query compiler at the time of creation.
+        """
+        self._parent = None
+        self._parent_qc = None
+
+    def set_parent(self, parent: Series | DataFrame) -> None:
+        """
+        Set the parent object and its query compiler.
+
+        Parameters
+        ----------
+        parent : Series or DataFrame
+            The parent object that the Index is a part of.
+        """
+        self._parent = parent
+        self._parent_qc = parent._query_compiler
+
+    def check_and_update_parent_qc_index_names(self, names: list) -> None:
+        """
+        Update the Index and its parent's index names if the parent's current query compiler matches
+        the recorded query compiler (`_parent_qc`).
+        """
+        if self._parent is not None and self._parent._query_compiler is self._parent_qc:
+            new_query_compiler = self._parent_qc.set_index_names(names)
+            self._parent._update_inplace(new_query_compiler=new_query_compiler)
+            # Update the query compiler after naming operation.
+            self._parent_qc = new_query_compiler
+
+
 class Index(metaclass=TelemetryMeta):
 
     # Equivalent index type in native pandas
@@ -135,11 +170,8 @@ def __new__(
         index = object.__new__(cls)
         # Initialize the Index
         index._query_compiler = query_compiler
-        # `_parent` keeps track of any Series or DataFrame that this Index is a part of.
-        # `_parent_qc` keeps track of the original query compiler of the parent object.
-        # These fields are used with the name APIs.
-        index._parent = None
-        index._parent_qc = None
+        # `_parent` keeps track of the parent object that this Index is a part of.
+        index._parent = IndexParent()
         return index
 
     def __init__(
@@ -411,13 +443,6 @@ def __constructor__(self):
         """
         return type(self)
 
-    def _set_parent(self, parent: Series | DataFrame):
-        """
-        Set the parent object of the current Index to a given Series or DataFrame.
-        """
-        self._parent = parent
-        self._parent_qc = parent._query_compiler
-
     @property
     def values(self) -> ArrayLike:
         """
@@ -731,11 +756,9 @@ def name(self, value: Hashable) -> None:
             raise TypeError(f"{type(self).__name__}.name must be a hashable type")
         self._query_compiler = self._query_compiler.set_index_names([value])
         # Update the name of the parent's index only if the parent's current query compiler
-        # matches the recorded query compiler (_parent_qc).
-        if self._parent is not None and self._parent_qc is self._parent._query_compiler:
-            self._parent._update_inplace(
-                new_query_compiler=self._parent._query_compiler.set_index_names([value])
-            )
+        # matches the recorded query compiler.
+        if self._parent is not None:
+            self._parent.check_and_update_parent_qc_index_names([value])
 
     def _get_names(self) -> list[Hashable]:
         """
@@ -762,11 +785,9 @@ def _set_names(self, values: list) -> None:
             values = values.to_list()
         self._query_compiler = self._query_compiler.set_index_names(values)
         # Update the name of the parent's index only if the parent's current query compiler
-        # matches the recorded query compiler (_parent_qc).
-        if self._parent is not None and self._parent_qc is self._parent._query_compiler:
-            self._parent._update_inplace(
-                new_query_compiler=self._parent._query_compiler.set_index_names(values)
-            )
+        # matches the recorded query compiler.
+        if self._parent is not None:
+            self._parent.check_and_update_parent_qc_index_names(values)
 
     names = property(fset=_set_names, fget=_get_names)
 
diff --git a/src/snowflake/snowpark/modin/plugin/extensions/timedelta_index.py b/src/snowflake/snowpark/modin/plugin/extensions/timedelta_index.py
index 558e3bcee76..93efe292437 100644
--- a/src/snowflake/snowpark/modin/plugin/extensions/timedelta_index.py
+++ b/src/snowflake/snowpark/modin/plugin/extensions/timedelta_index.py
@@ -41,7 +41,7 @@
 from snowflake.snowpark.modin.plugin.compiler.snowflake_query_compiler import (
     SnowflakeQueryCompiler,
 )
-from snowflake.snowpark.modin.plugin.extensions.index import Index
+from snowflake.snowpark.modin.plugin.extensions.index import Index, IndexParent
 from snowflake.snowpark.modin.plugin.utils.error_message import (
     timedelta_index_not_implemented,
 )
@@ -118,8 +118,7 @@ def __new__(
             data, _CONSTRUCTOR_DEFAULTS, query_compiler, **kwargs
         )
         # `_parent` keeps track of any Series or DataFrame that this Index is a part of.
-        tdi._parent = None
-        tdi._parent_qc = None
+        tdi._parent = IndexParent()
         return tdi
 
     def __init__(
diff --git a/tests/integ/modin/index/test_name.py b/tests/integ/modin/index/test_name.py
index 33bc59739ff..f915598c5f6 100644
--- a/tests/integ/modin/index/test_name.py
+++ b/tests/integ/modin/index/test_name.py
@@ -358,12 +358,10 @@ def test_index_names_replace_behavior():
     """
     Check that the index name of a DataFrame cannot be updated after the DataFrame has been modified.
     """
-    data = (
-        {
-            "A": [0, 1, 2, 3, 4, 4],
-            "B": ["a", "b", "c", "d", "e", "f"],
-        },
-    )
+    data = {
+        "A": [0, 1, 2, 3, 4, 4],
+        "B": ["a", "b", "c", "d", "e", "f"],
+    }
     idx = [1, 2, 3, 4, 5, 6]
     native_df = native_pd.DataFrame(data, native_pd.Index(idx, name="test"))
     snow_df = pd.DataFrame(data, index=pd.Index(idx, name="test"))
@@ -389,3 +387,33 @@ def test_index_names_replace_behavior():
     # Compare the names. Changing the index name should not change the DataFrame's index name.
     assert snow_index.name == native_index.name == "test3"
     assert snow_df.index.name == native_df.index.name == "test2"
+
+
+@sql_count_checker(query_count=1)
+def test_index_names_multiple_renames():
+    """
+    Check that the index name of a DataFrame can be renamed any number of times.
+    """
+    data = {
+        "A": [0, 1, 2, 3, 4, 4],
+        "B": ["a", "b", "c", "d", "e", "f"],
+    }
+    idx = [1, 2, 3, 4, 5, 6]
+    native_df = native_pd.DataFrame(data, native_pd.Index(idx, name="test"))
+    snow_df = pd.DataFrame(data, index=pd.Index(idx, name="test"))
+
+    # Get a reference to the index of the DataFrames.
+    snow_index = snow_df.index
+    native_index = native_df.index
+
+    # Change and compare the names.
+    snow_index.name = "test2"
+    native_index.name = "test2"
+    assert snow_index.name == native_index.name == "test2"
+    assert snow_df.index.name == native_df.index.name == "test2"
+
+    # Change the names again and compare.
+    snow_index.name = "test3"
+    native_index.name = "test3"
+    assert snow_index.name == native_index.name == "test3"
+    assert snow_df.index.name == native_df.index.name == "test3"