Who says it doesn't exist? Who says it's occupational? The original Irish is Ó Fithcheallaigh. Don't worry about the -thch- business, consonants followed by the letter H tend to turn into a breathy sound, or disappear altogether. The name means "descendant of Fithcheallach", and that word means "chessplayer", hardly occupational. My opinion for, what it's worth, is that Fitheallach was here either a proper name, or it was a byname. That means that your ancestor, Fithcheallach, probably had another name but that was the name everybody knew him by, a sort of nickname. See if you can make something more readable out of that for your homework.