I am surprised to read, in many of the answers, that people have contacted state lottery commissions to learn what sort of trust, if any, may claim a prize.
This is essentially a legal question, and lottery commissions are not licensed to practice law.
If the question is unsettled in your jurisdiction, and if you ask a lottery commission whether or not you may claim through a trust, you may well get someone's guess of what the law is (an unqualified opinion) or what someone wishes the law were (a self-serving dictum), rather than a qualified response.
The response of the New Mexico lottery commission to Lilly's question (posted March 5 at 12:54 pm) is a case in point. In response to her question, "Can a winner [use] a trust to claim a prize?" The commission gave an unqualified and self-serving response:
A. The law requires the Commission to check the winner's name against a list.
B. If a trust claimed a prize, the Commission would not be able to do this.
So what? If the Commission has obligations, it isn't the trust's responsibilty to fulfill them. If the Commission is unable to identify the trust beneficiary, that's its problem. And, anyway, isn't the trust the winner? So, by giving the name and city of the trust, the Commission is able to fulfill its legal obligations. The intent of the law is of secondary importance; there are plenty of poorly-drafted laws. If our obligations were defined by what laws were supposed to say, rather than what they do say, we'd all have to be lawyers (and darn good ones, too).
In my opinion, anyone holding a winning ticket worth a substantial amount of money, such that anonymity is advisable, should consult an attorney of some repute who specializes in estate planning. You may have to fight the lottery commission, or the state itself; but in my opinion it's worth it. This is how rights are protected; this is how law works in the US. You don't just sit back and take the word of Joe Blow down at the bar, your best friend, your doctor, your wife, or the person you talked to at the Lottery Commission -- even if the person you talked to was an attorney for the Commission, which is your adversary in this situation, not your friend. No, you get a lawyer and you fight like hell for your rights. Big companies, landlords, etc., trample on little guys ALL THE TIME, because they are convinced that little guys don't have the stomach or the resources to fight; and most of the time they're right. You have a lot to protect in your anonymity as a multi-million-dollar winner. It's not just the freeloaders and deadbeats you have to worry about. The Mexican Mafia is crossing the border, kidnapping rich people in the US, taking them back to Mexico, torturing them and holding them for ransom.
So fight. You may set the precedent in your state. And your anonymity, as a winner, is without price.