About a third allow fully anonymous claims.

Even the ones that don't, in many (perhaps most) trusts can claim it. So winners set up a trust, and lawyers working for the trust claim it on behalf of the trust.

So the 'winner' might be two guys in really good suits with the name "ABC Trust". Now, the lawyers have to attest to a whole bunch of shit to ensure it's not an ineligible winner hiding behind the trust, but a big-name law firm isn't going to perjure themselves over what's really a pretty small amount of billable hours. THEY aren't winning tens or hundreds of millions.

Because if you win even a few million, a good law firm and account is worth every penny just for the work they'll do, but not having every dumb fuck you went to school with known you won is goddamn priceless.