badger (n.)
1520s, perhaps from bage "badge" (see badge) + -ard "one who carries some action or possesses some quality," suffix related to Middle High German -hart "bold" (see -ard). If so, the central notion is the badge-like white blaze on the animal's forehead (as in French blaireau "badger," from Old French blarel, from bler "marked with a white spot;" also obsolete Middle English bauson "badger," from Old French bauzan, literally "black-and-white spotted"). But blaze (n.2) was the usual word for this.

An Old English name for the creature was the Celtic borrowing brock; also græg (Middle English grei, grey). In American English, the nickname of inhabitants or natives of Wisconsin (1833).
badger (v.)
1790, from badger (n.), based on the behavior of the dogs in the medieval sport of badger-baiting, still practiced in 18c. England. Related: Badgered; badgering.