Least-populated city in Northern Ireland, that gives its name to the county it's located in (6)
I believe the answer is:
armagh
(Other definitions for armagh that I've seen before include "Irish county for Graham" , "Seat of all-Ireland bishopric" , "County S. of L. Neagh" , "Town where all-Ireland bishopric is located" , "Seat of Archbishop of All Ireland" .)