This question already has an answer here:
I first saw the idea on a different question. Can't remember where exactly it was. It may even have just been a joke but the idea seems interesting, although there's probably a very delicate border between this being tasteful vs annoying.
More specifically, would it be possible to to be a, for example, chaotic evil wizard but have the party convinced that you're a good-aligned bard or other?
Assume the DM knows what you're doing. It's the rest of the party you're trying to fool.
Also note: this idea is not meant for a long-run campaign. It's for a campaign meant to last two or three sessions max.
Another edit: Wizard/Bard is not set in stone. We currently aren't too sure what classes would make this easiest to pull off, but the short nature of the campaign makes us believe that lying about the character's class might be doable.