It is a Germanic name consisting of the two elements hadu "battle, combat" and wig "fight, duel".
The name is on record since the 9th century, with Haduwig, a daughter of Louis the German.
The name remained popular in German high nobility during the 10th and 11th centuries.
Other medieval spellings include Hathuwic, Hathewiga, Hadewich, Hadewic, Hathwiga, Hadwich, Hatwig, Hadwig, Hediwig, Hedewiga, Hedewich, Hedewiih, Hatuuih, Hetvic, Haduwich, Hadawich, Hatuwig, etc.
[1] A common German (and also Dutch) diminutive of Hedwig is Hedy.