Fuller \f(ul)-ler\ as a boy's name is of Old English origin, and the meaning of Fuller is "one who shrinks cloth". Occupational name. The woolen fabric that was a staple of the medieval English economy had to be treated by fullers before it was made into clothes.
Baby names that sound like Fuller are Fowler and Waller. Other similar baby names are Muller, Buhler, Bueller, Fylmer, Filmer, Folker, Fulke, Heller, Hiller, Keller, Cuyler, Loller, Miller, Myller, Mueller and Quiller.