Derived from Welsh gwalch “hawk”, possibly combined with mei “May (the month)”. This is the name of a character in Welsh legend. He is probably the antecedent of Gawain from Arthurian romance.
From Japanese 葵 (aoi) meaning “hollyhock, althea” or an adjectival form of 碧 (ao) meaning “green, blue”. Other kanji with the same reading can form this name as well.