Perhaps the Doctor wasn't being quite literal when he addressed Dalton's character. It's possible the President's actual name was something completely different, but by calling him "Rassilon", the Doctor was speaking derisively, comparing the man's policies to those of Rassilon.
RTD confirmed the character's name is Rassilon. But, to my knowledge he hasn't commented one way or the other if he's that Rassilon or someone else named Rassilon. We all just assume he is that Rassilon, since there's no reason why he can't be.
I dug around a bit after this, and found references to sections of "A Writer's Tale" that seem to indicate that Dalton's character was both named Rassilon and intended to be the "historical" character. Unfortunately, I can't find exact quotes including context, so it's difficult to determine if this is absolutely the case or if it contains high concentrations of reader interpretation. There may still be a bit of wiggle room, but until I know more, I'll give up this argument.