What is the best way to claim a winning lottery ticket anonymously?
I'm sure you won't have that problem, but just in case:
Several states allow the price to be claimed anonymously. It is unclear if the lottery company wouldn't know who you are, but it definitely means that the public and the press would not know who you are.
In the other states, you could send a lawyer with a power of attorney to handle it for you, or found a trust that receive the money, without your name being publicly on it.
However, typically you signed away your rights to anonymity by buying a lottery ticket - you agreed that if you win, the lottery company can use you picture, video, and name for advertisements, and sometimes you are even required to cooperate (meaning show up, dress nicely, and smile when they take the pictures/videos), otherwise, you simple don't get the winning price. You can read this in the fine print on their website; each state will be probably very different.
Although the lottery company might not report you to the IRS, they will keep the highest possible tax rate from your winnings (and send them to the IRS).
If you never file with the IRS after that, you effectively overpaid on taxes, so the IRS couldn't care less who you are.
Probably the best approach is to sit the circus out, and move afterwards to a different state or country.
It will depend on the state. Most states do not allow anonymous winners for purposes of transparency and trust. Would you want someone from the Lottery Commission to rig the lottery in their favor and claim the prize anonymously?
One way to possibly hide your true identity is to create a Blind Trust, and claim the winnings in the name of the trust. Again, though, some states may not allow this for the same reasons.