R create serial number based on two different columns

Question

I wanted to create serial number based on two different columns. 'item' should be assigned serial number based on each 'name'. Please let me know how to do this.

name <-  c('Name1', 'Name1', 'Name2', 'Name2', 'Name2', 'Name3', 'Name3', 'Name3')
item <-  c('item1' , 'item2' , 'item1','item2','item3','item1','item1','item3')

     name  item
1 Name1 item1
2 Name1 item2
3 Name2 item1
4 Name2 item2
5 Name2 item3
6 Name3 item1
7 Name3 item1
8 Name3 item3

Expected out put.

  name  item sl.no
1 Name1 item1     1
2 Name1 item2     2
3 Name2 item1     1
4 Name2 item2     2
5 Name2 item3     3
6 Name3 item1     1
7 Name3 item1     1
8 Name3 item3     2