BUG: rename fails when using level

doc/source/whatsnew/v1.4.0.rst

@@ -413,6 +413,7 @@ Interval
 
 Indexing
 ^^^^^^^^
+- Bug in :meth:`Series.rename` when index in Series is MultiIndex and level in rename is provided. (:issue:`43659`)
 - Bug in :meth:`DataFrame.truncate` and :meth:`Series.truncate` when the object's Index has a length greater than one but only one unique value (:issue:`42365`)
 - Bug in :meth:`Series.loc` and :meth:`DataFrame.loc` with a :class:`MultiIndex` when indexing with a tuple in which one of the levels is also a tuple (:issue:`27591`)
 - Bug in :meth:`Series.loc` when with a :class:`MultiIndex` whose first level contains only ``np.nan`` values (:issue:`42055`)

pandas/core/generic.py

@@ -1147,7 +1147,11 @@ def rename(
 
             # GH 13473
             if not callable(replacements):
-                indexer = ax.get_indexer_for(replacements)
+                if ax._is_multi and level is not None:
+                    indexer = ax.get_level_values(level).get_indexer_for(replacements)
+                else:
+                    indexer = ax.get_indexer_for(replacements)
+
                 if errors == "raise" and len(indexer[indexer == -1]):
                     missing_labels = [
                         label

pandas/tests/series/methods/test_rename.py

@@ -4,6 +4,7 @@
 
 from pandas import (
     Index,
+    MultiIndex,
     Series,
 )
 import pandas._testing as tm
@@ -101,3 +102,26 @@ def test_rename_callable(self):
         tm.assert_series_equal(result, expected)
 
         assert result.name == expected.name
+
+    def test_rename_series_with_multiindex(self):
+        # issue #43659
+        arrays = [
+            ["bar", "baz", "baz", "foo", "qux"],
+            ["one", "one", "two", "two", "one"],
+        ]
+
+        index = MultiIndex.from_arrays(arrays, names=["first", "second"])
+        s = Series(np.ones(5), index=index)
+        result = s.rename(index={"one": "yes"}, level="second", errors="raise")
+
+        arrays_expected = [
+            ["bar", "baz", "baz", "foo", "qux"],
+            ["yes", "yes", "two", "two", "yes"],
+        ]
+
+        index_expected = MultiIndex.from_arrays(
+            arrays_expected, names=["first", "second"]
+        )
+        series_expected = Series(np.ones(5), index=index_expected)
+
+        assert result.equals(series_expected)