Duplicate Sequence Number For Identical Rows

I have a table:

Name
_____
Smith Street
Smith Street
John Street
Ed Street
Ed Street
Ed Street

and need to assign sequence numbers only when the record (Name) changes, e.g. :

Name Seq
_____ ____
Smith Street 1
Smith Street 1
John Street 2
Ed Street 3
Ed Street 3
Ed Street 3

I have experimented with row_number partition but then i just get the sequence returning to 1 when the name value changes.

If I grouped the records by Name I would like to have unique, sequential numbers: 1, 2, 3 but where there is the same name I would like the sequence to stop and the number to replicate?