Actually only a few (seven) states allow anonymity in claiming lottery prizes:
https://abcnews.go.com/US/win-mega-millions-16-billion-jackpot-states-remain/story?id=58623192
I don’t know if other states can prevent you from legally claiming it through a trust, though. There was a case in New Hampshire where a winner got a judge to authorize permanent anonymity, even though NH state law specified that winners must be public AND the winner had signed the ticket.
So maybe it is still open to some legal battles in other states if someone wins and plays their cards right with a lawyer and private trust set-up.
Lucky for me, I live in one of those states.
I think that it is ridiculous that winners should be publicized. There are way too many problems with that, from leeching relatives to strangers who would scam them for everything.