df = pd.DataFrame({'a': [0], 'b': [1]})
ser = df['b'].rename(None)
print(ser.groupby(df['a']).apply(lambda x: x))
df = pd.DataFrame({'a': [0, 1], 'b': [1, 2]})
ser = df['b'].rename(None)
print(ser.groupby(df['a']).apply(lambda x: x))
produces
0 1
Name: 0, dtype: int64
0 1
1 2
dtype: int64
In the first case, the name attribute on the resulting Series is set as 0, the group. In the second case, the two groups have different names and so the correct name attribute of None is on the result. The name attribute should be None in the first case as well.
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