the only ref I have to Bermingham
is The powerful Anglo-Norman family of Bermingham, Barons of Athenry, took the name of MACFEORAIS or MACORISH from an ancestor PIERCE, PIERAS, or FEORAS, the son of Meyler Bermingham.~-
from http://www.ee.surrey.ac.uk/Contrib/manx/manxnb/v11p113.htm talking about Kerruish/Corris

Birmingham of course immediately brings up the UK city in any search