df =
     name  amount  date
 0     A     10      1
 1     B     15      1
 2     A      5      2
 3     C      7      3
 4     A      8      4
 5     B     10      4
 6     C     11      4

df_result =
     name  amount  date
 0     A     10      1
 1     B     15      1
 2     A     15      2
 3     B     15      2
 4     A     15      3
 5     B     15      3
 6     C      7      3
 7     A     23      4
 8     B     25      4
 9     C     18      4

>>> df.groupby(by=['name','date']).sum().groupby(level=[0]).cumsum().reset_index()
  name  date  amount
0    A     1      10
1    A     2      15
2    A     4      23
3    B     1      15
4    B     4      25
5    C     3       7
6    C     4      18