This is a mainly Scots surname, and has a dual origin in that country - i) It is the name of an Aberdeenshire family that claims descent from the MacDonalds. If this is the case then the name would probably the old Gaelic male given name Conn, meaning unknown to me. ii) It is an altered form of the Ayrshire name Petcon, which is from a place name. Elsewhere there are some Conns in Ireland whose name is alleged to have originated as MacMhiolhcon, which became McIlchon, then Conn. I susect that most Irish Conns would be of Ulster Scots descent, most likely from the more numerous Ayrshire family. In addition I believe that Conn has been adopted on occasion in the US as a substitute for Cohen.