you need to access the index's properties
df.index.name = 'id'
original
student count
summary
0 error 6
1 yes 1
2 no 1
3 other 9
fixed df:
student count
id
0 error 6
1 yes 1
2 no 1
3 other 9
Update: seems like you had a name for the column's index. You should remove it with
df.columns.names = ''