I know that it has been a long time since you posted this request. But here is what I have on the Finn name in my records.
An Ann Finn arrived in New York from County Cork Ireland, Myross Parish, Listarken, Village of Union Hall sometime during the Potato Famine with her mother and sister(no names). The father had come over prior to their arrival. (Not sure when)They eventually settled in Buffalo. She married a Charles Benzene who was killed or died when she was pregnant with a son. Ann married Charles friend, Edward and had 5 children total. Her sis ter is believed to have become a nun after coming to the States. No info on either or her parents or their names.