Contra the others posting here, I don't think there is much to be gained by pretending to be something you're not.
Outlaws: No one except an Outlaw will shoot at the Sheriff, which means that if the Outlaws hold their fire, the Sheriff will sit there unhurt while everyone else gets whittled down. At the same time, the Outlaws' best bet is to concentrate fire and overwhelm the Sheriff's ability to Missed! and Beer their attacks. Therefore, your best play is to open fire as soon as all Outlaws are able to hit the Sheriff, and keep shooting till the Sheriff dies. This of course means revealing yourselves.
Sheriff: Everyone knows who you are.
Deputy: There is very little down side to having people know you're the Deputy. The Outlaws want to kill the Sheriff; you are a mere annoyance. The Sheriff is on your team. The only one who is gunning for you personally is the Renegade, and the only way to fool the Renegade is to pretend to be an Outlaw, which would be insane (your own Sheriff would be trying to kill you).
Renegade: This is the one person who wants to hide his/her identity. Renegades always pretend to be Deputies at first. However, the key to Renegade victory is killing the Deputy early; if you "play Deputy" and only shoot at Outlaws, you will then have to go head-to-head with the real Deputy, while the Sheriff drinks beer and reloads to finish you off. You have to kill the Deputy before the Outlaws die, at which point you can't very well pretend to be the Deputy any more! So your deception has a limited shelf life.
The hidden identity part of "Bang!" is not really a big part of the game. It adds some uncertainty in the opening turns, but once the Outlaws make their move, things come clear pretty quickly. Most of the strategy is about managing your hand, picking your targets, and choosing what to play when. (It's not a very deep game, nor is it intended to be; it's a party game, fast and simple and fun. If you want a game that challenges your strategic skills, Bang! ain't it.)