Fagin/Fagan is Irish. Do your geneology homework and eventually you will find a census entry where the parents are noted as being "born in Ireland."
I search the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840, rare B4 1800. Note - without a known county, there is AT LEAST a 35% chance your ancestors rcds aren't in the database.
For the surname Fagan there are 9,531 B rcds dating from 1719 and 4,735 M rcds dating from 1731.
Google the Foundation's name to lead you to this database. Register, opt to be notified as rcds are added and browse. Pls post your search results to my genforum msg.