It depends how well-known you have to be to be well known, but for some level of well-known, off the top of my head: Leiber and Stoller, Ashford and Simpson, N

It depends how well-known you have to be to be well known, but for some level of well-known, off the top of my head: Leiber and Stoller, Ashford and Simpson, Nile Rodgers and Bernard Edwards, Rod Temperton, Diane Warren, Desmond Child, and Max Martin are well known songwriters from more modern times. However, their hits are much better known than they are, compared to the great American songbook guys. Although there are other very successful songwriters from that era with less name recongnition, for example, Johnny Mercer or Harry Warren.