Are the noun "badger", naming an animal, and the verb "to badger", describing the behavior of a person, related etymologically? Does the meaning of one come directly from the other?
What about the word "badge"?
the verb is actually derived from the noun, here's the noun:
1520s, from M.E. bageard, perhaps from bage "badge" + -ard "one who carries some action or possesses some quality," suffix related to M.H.G. -hart "bold" (see -ard). If so, the central notion is the badge-like white blaze on the animal's forehead (cf. Fr. blaireau "badger," from O.Fr. blarel, from bler "marked with a white spot"). But blaze (2) was the usual word for this. An O.E. name for the creature was the Celtic borrowing brock; also græg (M.E. grei, grey). In Amer.Eng., the nickname of inhabitants or natives of Wisconsin (1833).
and here's the verb (refers to noun):
1794, from badger (n.), based on the behavior of the dogs in the medieval sport of badger-baiting. Related: Badgered; badgering.
The verb badger, as with dog, ferret, weasel, bug, ram, hog, slug, crow, crab, parrot, squirrel, porpoise, bull, and buffalo, comes from the (alleged) behavior or treatment of the animal (as do pig out, monkey with, horse around, rat out, outfox, and cat about). Hunting for a particular animal gets its name from mouse, whale, fish, and (less commonly) moth, owl, and bird.
The same is not true of cow, grouse, and quail, and (less surprisingly) swallow, sow, and bear — the animal and the verb are etymologically unrelated.
The only common animal name that I found that comes the other way is sloth (the animal was named after the sin), but I'm on the look-out for more. (In Silence Of The Lambs a character claims that "moth" originally meant "to destroy", but I can't find a cite.)
The verb butterfly is a culinary term meaning to cut something open, so it (vaguely) resembles a butterfly, said of mostly shrimp and chicken breast. It's the only example I have found of an animal name meaning "to make resemble the animal", unless you count spread-eagle.