I had a discussion with a friend and we both ended up agreeing that it recklessly endangers a lottery winner to publicly reveal their identity. If that person becomes robbed, hacked and/or injured soon after winning as a result of being revealed, can't they sue the state government for being so blatantly careless?
Unfortunately I don't have the rep for a comment, but a quick google search would reveal there is at least precedence of remaining anonymous in a "Right to Know" law state (is the correct term? I'm not a US citizen, nor have any legal background) in the case of Jane Doe vs New Hampshire Lottery Commission
While this doesn't cover any part of suing the state as mentioned above, it does cover the underlying reason why you would likely be unsuccessful in attempting it, namely the freedom of information that is allowed to citizens of most US states.
The level of anonymity or privacy given by the lottery administrator (the state) to the lottery winner depends on the terms and conditions of lottery that are accepted as a binding contract when the buyer buys a lottery ticket. It's all in the small print. If you don't like the terms of the lottery, don't buy a ticket.
The lottery terms probably says that the state can use the winner's name in marketing and promotional materials. For a winner to be able to be anonymous, the terms of the lottery would have to specifically state that anonymity is guaranteed, while at the same time, allowing the state to report the winner to the IRS for tax purposes. (Delaware, Kansas, Maryland, North Dakota, Ohio and South Carolina all allow lottery winners to remain anonymous.)
The winner will have little recourse against the state due to circumstances - like being robbed or fleeced - which are outside of the state's control because they are actions by individuals, not the state. The state is also not guilty of "recklessly endangering people" because the ticket buyer knowingly bought a ticket, hoping to win, and agreed to terms.
And it's quite difficult to sue any form of government; states and the federal government are by law immune to most legal actions. The recourse of the ticket buyer - or group of buyers who were possibly harmed as a result of winning - is to encourage the legislation of laws that provide for the anonymity of winners.