Cohen is also an Irish surname that's not related with the Hebrew one like other comments pointed out. It's recorded in Robert Bell's "The book of Ulster surnames" on page 43 as a version of Cowan or Coyne, same as in Edward MacLysaght “The surnames of Ireland” on page 50 and in Ida Grehan's "The dictionary of Irish family names" on page 72 as a version of Coyne. It think that should be added to the description.
Cohen is NOT an exclusively Jewish surname. In MacLysaght's "The Surnames of Ireland" it says Cohen is used as a form of Coyne (ultimately from Irish Gaelic "wild goose") in Connacht and of Cowan in County Down. MacLysaght says the name "has usually no Jewish connotation in Ireland."And though Cohen is the most common form of the Hebrew surname when written in the letters of the Roman alphabet, there are a great many others, (Kohen, Kohn, Cahan, Cahn, Cahen, Kahn, Kahen, Cohane, Kahan, Kahane, Cohani, Cahani, Cahany, Kahany, Cogan, Kogen, Kogan, Cagan, Kagan, etc.) No culture can really have a monopoly on any short name -- there is bound to be another word or name in another culture somewhere which resembles it just by chance.