The English surname Gomme is similar, originating from the Old English guma, Middle English gome meaning man.. Gomez is the 68th most popular surname in the United States and the 15th most common Hispanic surname.ind records, queries, and lineage-linked family trees posted for the Gomez surname and its variations. GOMEZ Surname & Family Mailing Lists. RootsWeb hosts several free mailing lists for researchers of the Gomez surname.