Nice post, Myridon, which clears that up. I later thought the surname might come from a character trait and nickname ie someone who badgers people, but clearly not. Where did this sense come from? I can only find definitions not explanations. Are badgers tenacious and annoyingly persistent in their behaviour? They are secretive and avoid human contact so how could this be established and become a verb? OED?

The OED2 says it is probably a reference to human treatment of badgers, baiting them and drawing them from their holes, although possibly influenced by an old folk belief that, once a badger had bitten, it would not release its bite until its teeth met.  Another possible influence but not a likely origin, acc. to the OED, is another meaning of “badger”, meaning a trader or peddler (as mentioned by Myridon), and the derived verb meaning to trade thus, to haggle or drive a hard bargain.

FWIW, the Italian family of Tasso from Camerata Cornello (to which the poet belonged and which is related to the German Thurn und Taxis family) traces their name to tasso ‘badger’ as evidenced by the badger on their escutcheon (link).

I can’t understand the German text, jheem, but was etymology a big deal then, and is their trace convincing? Could it have been a family pun based on a homonym? Great find, though.

but was etymology a big deal then, and is their trace convincing? Could it have been a family pun based on a homonym?

I just assumed it was what they felt. And, yes, it could be a pun. Maybe it was easier for them to draw a badger than a yew tree. And, yes, it could’ve been a third word meaning we know not what.

"Canting” or punning coats of arms were commonplace, and etymology didn’t come into it. For example, the surname Bowes if actually topographical in origin, meaning something like “river bends”, but the Bowes family coat of arms is three longbows, and the name Lucey derives from the placename Luce in Normandy but the coat of arms is three pikes, or “luces”. So the Tasso family’s using a badger doesn’t necessarily imply that the name derived from a word for badger, or even that the family thought it did.

Returning to our badgers, I see that etymonline says (under texture)

t… from PIE base *tek- “to make” (cf. Skt. taksati “he fashions, constructs,” taksan “carpenter;"… Gk. tekton “carpenter,” tekhne “art;” O.C.S. tesla “ax, hatchet;” Lith. tasau “to carve;” O.Ir. tal “cooper’s ax;” O.H.G. dahs, Ger. Dachs “badger,” lit. “builder (my emphasis)…

so the badger was seen as a builder, presumably because of his extensive setts ... I wonder why English borrowed the Celtic word, to call him Brock? I read somewhere long ago the theory that “brock” comes from the “brrk brrk” noise the animal makes (rather than from a word meaning “white”, as the OED suggests), though I have no idea (never having been that close to a badger) if it does indeed make such a noise ...