The "Robin" name is more important to the idea of Batman's successor anyway, as evidenced by as many as five characters having taken on that persona (with a potential sixth on the horizon).
It was fan service AND pandering to the audience. It was an acknowledgement of the Robin character in the Nolanverse. Kind of a big deal for some of us.
As I said, I don't think the general audience wouldn't have gotten the message by the end.
And how would calling him Dick Grayson or Tim Drake make it any less of an acknowledgment of the Robin character in the Nolanverse for the fans? It would've been an even better easter egg IMO.
Also, I hope I don't sound like I think this is a huge problem. It isn't. It's more of a small personal inconvenience.
