Depends on how badly I behave. It's perfectly well within my rights to call anyone in the bar a cunt. Some might be offended. There might be an argument. I might be asked to leave. There might even be fisticuffs. But at no point during any of that will my real identity matter an iota.
But if you were able to come back into the bar in a disguise a minute later, they would want to know your real identity to prevent you from coming back.