Technically, your designs are copyrighted once they are in fixed form. And you can gain common law trademark rights to your brand name or logo as you use it in commerce. So you do have some level of legal recourse even without any official copyright or trademark registration.
But as Charles mentioned, what are you really going to do if someone steals your designs or logo?
Reality is, printers are in the business of printing, not stealing. You are more valuable to them as a paying customer. So it's probably a waste of time to have them sign an agreement. But if it makes you feel better, you can ask them. They will probably just do it to please you than waste time being offended about it.