If you are a recreational pilot any adult can fly your drone without the requirement they have their own unique registration number. To me, the question is are you responsible for their proper operation?
As a recreational flyer, I don't think you are responsible for the other person's violation of aviation regulations (from the FAA), but if you loan your property (here, the drone) to someone else, and they injure another person with it, prepared to be included on the inevitable tort lawsuit.