diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 1abb01099f977..5b2088e995d51 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -1152,7 +1152,7 @@ def rename(
                     ]
                     raise KeyError(f"{missing_labels} not found in axis")
 
-            new_index = ax._transform_index(f, level)
+            new_index = ax._transform_index(f, level=level)
             result._set_axis_nocheck(new_index, axis=axis_no, inplace=True)
             result._clear_item_cache()
 
diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py
index c5d5d5a301336..d12366caa44e3 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -490,7 +490,7 @@ def __init__(
                 self.grouping_vector,  # Index
                 self._codes,
                 self._group_index,
-            ) = index._get_grouper_for_level(mapper, ilevel)
+            ) = index._get_grouper_for_level(mapper, level=ilevel)
 
         # a passed Grouper like, directly get the grouper in the same way
         # as single grouper groupby, use the group_info to get codes
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 6070d6863039e..0a1d624894929 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -1500,7 +1500,7 @@ def _validate_names(
     def _get_names(self) -> FrozenList:
         return FrozenList((self.name,))
 
-    def _set_names(self, values, level=None) -> None:
+    def _set_names(self, values, *, level=None) -> None:
         """
         Set new names on index. Each name has to be a hashable type.
 
@@ -1906,7 +1906,7 @@ def _drop_level_numbers(self, levnums: list[int]):
                 verify_integrity=False,
             )
 
-    def _get_grouper_for_level(self, mapper, level=None):
+    def _get_grouper_for_level(self, mapper, *, level=None):
         """
         Get index grouper corresponding to an index level
 
@@ -1915,7 +1915,7 @@ def _get_grouper_for_level(self, mapper, level=None):
         mapper: Group mapping function or None
             Function mapping index values to groups
         level : int or None
-            Index level
+            Index level, positional
 
         Returns
         -------
@@ -5642,7 +5642,7 @@ def map(self, mapper, na_action=None):
 
     # TODO: De-duplicate with map, xref GH#32349
     @final
-    def _transform_index(self, func, level=None) -> Index:
+    def _transform_index(self, func, *, level=None) -> Index:
         """
         Apply function to all values found in index.
 
@@ -5651,6 +5651,7 @@ def _transform_index(self, func, level=None) -> Index:
         """
         if isinstance(self, ABCMultiIndex):
             if level is not None:
+                # Caller is responsible for ensuring level is positional.
                 items = [
                     tuple(func(y) if i == level else y for i, y in enumerate(x))
                     for x in self
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index cac0a8cc5791f..7ae5300eb34f1 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -761,6 +761,7 @@ def levels(self) -> FrozenList:
     def _set_levels(
         self,
         levels,
+        *,
         level=None,
         copy: bool = False,
         validate: bool = True,
@@ -954,6 +955,7 @@ def codes(self):
     def _set_codes(
         self,
         codes,
+        *,
         level=None,
         copy: bool = False,
         validate: bool = True,
@@ -1392,7 +1394,7 @@ def format(
     def _get_names(self) -> FrozenList:
         return FrozenList(self._names)
 
-    def _set_names(self, names, level=None, validate: bool = True):
+    def _set_names(self, names, *, level=None, validate: bool = True):
         """
         Set new names on index. Each name has to be a hashable type.
 
@@ -1473,7 +1475,7 @@ def _set_names(self, names, level=None, validate: bool = True):
     # --------------------------------------------------------------------
 
     @doc(Index._get_grouper_for_level)
-    def _get_grouper_for_level(self, mapper, level):
+    def _get_grouper_for_level(self, mapper, *, level):
         indexer = self.codes[level]
         level_index = self.levels[level]