Print names on Irregular paper?

HelloI would like to know if there was a device out there that will allow me to print a name on irregular sized, glossy, thick, fancy paper, that won’t fit into my printer. It needs to look professional and like I sent it out to a printing company to have it personally imprinted with there name on it, but since I don’t know their names in advance, and the fact that it will be different names each day, I can’t have then professionally printed up. Is there some small hand held device, like a label maker that will print on stuff? Thanks