Because of many of the problems associated with publicity, many states allow winners to claim their prize anonymously. On top of that, I live on the opposite coast as my family. They would never know.
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.