Never seen a moped license, but most people I know with a moped have a regular drivers license. NH has moped plates, the whole process is done through the DMV -- extremely cheap to register them too. Definitely call the DMV and inquire there, best way to do it. Theres a moped shop in Portsmouth too, Port City Mopeds, and you could ring them and ask if they might know, but better off just calling the DMV.