Badge
late Middle English: of unknown origin.
wiktionary
From Middle English badge, bagge, bage, bagy, from Anglo-Norman bage or Medieval Latin bagea, bagia(“sign, emblem”), of uncertain origin. Possibly derived from Medieval Latin baga(“ring”), from Old Saxon bāg, bōg(“ring, ornament”), from Proto-Germanic *baugaz(“ring, bracelet, armband”); or possibly the Anglo-Norman word is derived from an earlier, unattested English word (compare Old English bēag(“ring, bracelet, collar, crown”). Cognate with Scots bagie, badgie, bawgy(“badge”).
etymonline
badge (n.)
"token worn to indicate the wearer's occupation, preference, etc.," especially "device worn by servants or followers to indicate their allegiance," from Anglo-French bage (mid-14c.) or Anglo-Latin bagis, plural of bagia "emblem," all of unknown origin. Figurative sense "mark or token" of anything is by 1520s.
