BUG: Bug fix for GH48567
Groupby for Series fails if an entry of the index of the Series is equal to the name of the index. Analyzing the bug, I think the following small change would solve the issue:

diff --git a/pandas/core/groupby/grouper.py b/pandas/core/groupby/grouper.py index 5fc713d84e..9281040a79 100644
--- a/pandas/core/groupby/grouper.py
+++ b/pandas/core/groupby/grouper.py
@@ -875,7 +875,7 @@ def get_grouper(
             exclusions.add(gpr.name)

         elif is_in_axis(gpr):  # df.groupby('name')
-            if gpr in obj:
+            if not isinstance(obj, Series) and gpr in obj:
                 if validate:
                     obj._check_label_or_level_ambiguity(gpr, axis=axis)
                 in_axis, name, gpr = True, gpr, obj[gpr]

From my point of view "gpr in obj" does not make sense for series at this point. I think the if-statement is written for dataframes to look if gbr is one of the columns. Skipping the if-statement for series gives the correct results for the examples above. The testsuite for series and groupby runs without errors after the change. I added a test to the test suite at the end of pandas/tests/groupby/test_groupby.py and a comment in the BUG section to doc/source/whatsnew/v1.6.0.rst.

- [x] closes #48567 (Replace xxxx with the Github issue number)
- [x] [Tests added and passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#writing-tests) if fixing a bug or adding a new feature
- [ ] All [code checks passed](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#pre-commit).
- [ ] Added [type annotations](https://pandas.pydata.org/pandas-docs/dev/development/contributing_codebase.html#type-hints) to new arguments/methods/functions.
- [x] Added an entry in the latest `doc/source/whatsnew/vX.X.X.rst` file if fixing a bug or adding a new feature.

Thanks @JanVHII 