I would expect it depends on if you're booking yourself as an artist with an identity or as a musician for hire. In other words, shows I get hired to do are events that want to book Rory Hoffman the artist. They are not looking to hire any musician, regardless who he is, just so there is music at their event. If you're trying to become an artist with a name, you might want to pick a look and stick with it, modifications allowed of course. If you hire Allen Jackson to do a show you have a pretty good idea what he's going to look like. But if the gig isn't about you, but you're more of an anonymous person performing a service, then by all means fit in to the situation you're hired to play.