Improve MultiIndex label rename checks

doc/source/whatsnew/v3.0.0.rst

@@ -909,6 +909,7 @@ Other
 - Bug in :meth:`DataFrame.sort_values` where sorting by a column explicitly named ``None`` raised a ``KeyError`` instead of sorting by the column as expected. (:issue:`61512`)
 - Bug in :meth:`DataFrame.transform` that was returning the wrong order unless the index was monotonically increasing. (:issue:`57069`)
 - Bug in :meth:`DataFrame.where` where using a non-bool type array in the function would return a ``ValueError`` instead of a ``TypeError`` (:issue:`56330`)
+- Bug in :meth:`Index._transform_index` where transformations are applied across all levels one by one even when a level is not specified (:issue:`55169`)
 - Bug in :meth:`Index.sort_values` when passing a key function that turns values into tuples, e.g. ``key=natsort.natsort_key``, would raise ``TypeError`` (:issue:`56081`)
 - Bug in :meth:`MultiIndex.fillna` error message was referring to ``isna`` instead of ``fillna`` (:issue:`60974`)
 - Bug in :meth:`Series.describe` where median percentile was always included when the ``percentiles`` argument was passed (:issue:`60550`).

pandas/core/indexes/base.py

@@ -6429,12 +6429,15 @@ def _transform_index(self, func, *, level=None) -> Index:
         Only apply function to one level of the MultiIndex if level is specified.
         """
         if isinstance(self, ABCMultiIndex):
-            values = [
-                self.get_level_values(i).map(func)
-                if i == level or level is None
-                else self.get_level_values(i)
-                for i in range(self.nlevels)
-            ]
+            if level is None:
+                return self.map(func)
+            else:
+                values = [
+                    self.get_level_values(i).map(func)
+                    if i == level
+                    else self.get_level_values(i)
+                    for i in range(self.nlevels)
+                ]
             return type(self).from_arrays(values)
         else:
             items = [func(x) for x in self]

pandas/tests/frame/methods/test_rename.py

@@ -164,6 +164,14 @@ def test_rename_multiindex(self):
         renamed = df.rename(index={"foo1": "foo3", "bar2": "bar3"}, level=0)
         tm.assert_index_equal(renamed.index, new_index)
 
+    def test_rename_multiindex_tuples_with_checks(self):
+        df = DataFrame({("a", "count"): [1, 2], ("a", "sum"): [3, 4]})
+        renamed = df.rename(
+            columns={("a", "count"): ("b", "number_of"), ("a", "sum"): ("b", "total")}, errors="raise"
+        )
+        new_columns = MultiIndex.from_tuples([("b", "number_of"), ("b", "total")])
+        tm.assert_index_equal(renamed.columns, new_columns)
+
     def test_rename_nocopy(self, float_frame):
         renamed = float_frame.rename(columns={"C": "foo"})