Duh. Yes, I know that. What I don’t know, anymore than you do, is whether the name on his arm referred to THAT Ishmael or something else. The common assumption that it must is just, well, dumb.
It’s not an altogether unreasonable inference. The kid could have had anything he wanted tatooed on his arm. Why did he chose that? I think it is unreasonable to conclude he chose it completely at random. There may be other explanations, and there is the obvious one.