It's an Irish name, that seemed to be the only solid explanation that we got.
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I'm not sure if this played a part in Angel's choosing of the name Connor but it is also very common as a surname, both as Connor and O'Connor. It's popular all over Ireland, including Galway where Angel is from. In its ancient, non-anglicisied form it would have been à“ Conchobhair or à“ Conchúir. There was a king of Ireland called Conchobhair and the name itself is associated with Irish royalty. Some sources describe the name meaning hero or champion, which would have been very fitting. Legends of the Conchobhair and the O'Connor's in general would surely have been told to Angel during his boyhood.