What does Cullen mean anyway?

Most people named Cullen are from Ireland, or have ancestors from Ireland, and I've read that the original name in Irish meant "holly tree", but others with the Irish name "whelp""small dog" have also been anglicized to Cullen.

And when I've been looking thru the records for my family from near Clogher, in County Tyrone, starting in 1860, my own ancestors seem to prefer to call themselves "Cullian", but they are also called Cullion, Cullen, Cullan, and even Cullinan.

Irish is hard@!