Fuller /ful-ler/ [2 sylls.] as a boys' 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. Kreatif forms: Fayler, Feler, Fulley.uller is a rare given name for males but a very popular surname for both adults and children (#256 out of 150436, Top 1%). (2000 U.S. Census). Presented below is the baby name popularity of Fuller for boys. Fuller has not been listed in the Top 1000 thus far. (2014 Birth Statistics).