"O'Neill's 1001 Tunes"

was, if I get my history correct, compiled by Captain O'Neill. Captain of the Chicago Police Force - collected mostly, if not all, from his officers - Irish ones at that.

As he put his name to it - I guess he has the say of it. So he does.

and anyway, as pointed-out, the O' denotes "son of" as in the Scots "Mac" and the English " 's" or more commonly Welsh - eg Evans, Williams, Jones etc.

And "daughter of" would be "ni" in whatever spelling.