GroupBy Doesn't Always Maintain Column Index Name

[WillAyd]

Just as a follow up to #29124 discovered during #29753 - looks like the column name is dropped for any/all and transformation functions in groupby

>>> df = pd.DataFrame([[1]], columns=pd.Index(["a"], name="idx"))
>>> df.groupby([1]).sum()
idx  a
1    1
>>> df.groupby([1]).any()
      a
1  True
>>> df.groupby([1]).shift()
    a
0 NaN

[marco-neumann-by]

Reading through the code example, I think this should be "GroupBy Doesn't Always Maintain Index Name".

[WillAyd]

Thanks! Updated to clarify