In an episode of HM, they mention that Robby Ray is Hannah's dad, but then several other episodes everyone seems to know that Robby Ray is Miley's dad, so wouldn't somebody have put two and two together?
The people who know that Robby Ray is Miley's dad, and the people who know that Robby Ray is Hannah's dad do not overlap much, and for the people who do, they haven't realized that they're the same Robby Ray. (Because of the same magical denial that is seen so often in the Wizards' part of this universe!)
And for that matter, if I'm wrong, and no one's ever said that Hannah's manager is also her dad, I know that in Mr. Jonas, Mr. Jonas, and Mr. Jonas she calls him "Robby Ray," and Rico wanted him to sign the Robby Ray album when he was trying to impress that girl, so if kids at school went nuts and tried to befriend Miley just because she was dating Jake Ryan, wouldn't they try and befriend her because her dad is Hannah Montana's manager?
Worse than that, actually. At least a few people do know that Hannah's manager is also her father, such as the photographer. The thing is that, obviously, the kids at school either don't know that Robby Ray is her father, or that Robby Ray is Hannah's Manager. They couldn't, or they would know Too Much. (Random Capitals are Cool, by the way.) Furthermore, Robby Ray is portrayed as more or less a one-hit wonder who is more or less all washed up now (gee, I wonder who that reminds us of :P). It's unlikely that any of the kids at school really know of him.
And why wear the mustache if he's still "Robby Ray?"
The mustache helps to throw people off and make them think that he's possibly not the same Robby Ray. Alternatively, perhaps he was jealous that everyone else got a disguise.
Does any of that even make sense?
I think so, yes. Of course it's a bit of a stretch to remain in-universe – but I think the fact that we know for a fact magic exists in it helps alleviate that a little bit.