Fulbright \ful-bright, fulbr(ig)-ht\ as a boy's name is of Old German origin, and the meaning of Fulbright is "very bright". See Filbert. The name has become famous through the Fulbright Scholar program, which sends (very bright) American graduate students to study abroad.
Fulbright has 4 variant forms: Fulbert, Philbert, Philibert and Phillbert.