I bought a semi tractor on auction and received a title, not only
without my name, but also without any signature of the seller (which
is a company, not an individual, closing down a factory). The purchase
is 100% legitimate. When I was at the DMV registering a title for
something else, I observed that they did not check the signature in
any way (obviously).

If I decide to keep this tractor, which I likely would, should I just
have, say, my wife sign it with something, in order to re-register?

i