Your comfort level is the most important factor when getting a massage. First of all, you need to be able to relax. I always suggest new clients undress to their comfort level, whether that may be getting completely undressed, leaving under garments on or staying clothed. Massage therapists are trained for all these instances.
Even if you leave all your clothes on, I still cover you with a top sheet and perhaps a blanket. Again, it is what will make you comfortable, which is what this is about. Your paying for a service and you should be comfortable, relaxed and be open to accept healing.