Is his actual name (i.e. Makiri Zolgen) common knowledge? Because you know, he could just use that.
Common knowledge? No. Known by Sakura's family (or, at least, those members of it that were around at the time of the Grail War)? Yeah, definitely.
... I very much doubt Rin would trust him or see him as an ally in any capacity if she had an inkling he was really Zouken.
No, of course not (at least post-HF), but he would see
her as an ally....