Pandas left join with duplicates

I have a pandas data frame like

A = pd.DataFrame({'Name' : ['A', 'A','A'], 'Value' : [1,2,3]})
and another DataFrame 
B = pd.DataFrame({'Name': ['A', 'C', 'D', 'A', 'E', 'A'], 'Value1' :[1,2,3,4,5,6]})

When I merge these I get

A.merge(B, how='left', on='Name')

In [4]: A.merge(B, how='left', on='Name')
Out[4]: 
  Name  Value  Value1
0    A      1       1
1    A      1       4
2    A      1       6
3    A      2       1
4    A      2       4
5    A      2       6
6    A      3       1
7    A      3       4
8    A      3       6

Anyway to do this merge in a way such that first row with 'A' will match only with first row with 'A' in B, and second with second and third with third.
Final output like

  Name  Value  Value1
0    A      1       1
1    A      2       4
2    A      3       6

Thanks,

I tried doing left merge. I wasnt expecting anything different, but I am looking for a better way to do this.

Doing Inner join doesnt help either

A.merge(B, how='inner', on='Name')

  Name  Value  Value1
0    A      1       1
1    A      1       4
2    A      1       6
3    A      2       1
4    A      2       4
5    A      2       6
6    A      3       1
7    A      3       4
8    A      3       6

Deduplicate with groupby.cumcount and pass it to merge as secondary key:

A.merge(B, how='left',
        left_on=['Name', A.groupby('Name').cumcount()],
        right_on=['Name', B.groupby('Name').cumcount()]
       )#.drop(columns='key_1')

Output:

  Name  key_1  Value  Value1
0    A      0      1       1
1    A      1      2       4
2    A      2      3       6

You are requesting something that is not actually a join.

You can do something like this however:

pd.concat([A, B[B.Name == "A"].reset_index().Value1], axis=1)