Setting up a trust doesn't necessarily do anything to keep your name from being released. Some states specifically require that prizes be claimed in the name of an actual person. That might allow the trustor to claim, but it may not.
Changing your name isn't hard, but it's also not a private matter, and your original name may turn up; a court ordered name change requires publishing legal notices. As long as you aren't doing so for fraudulent purposes, you can use whatever name you want, without taking specific legal steps (think common law marriage). If you try to claim as "little bunny foofoo" your real name is going to come out, but Hollingsworth Andrew Smith IV should be able to claim as Andrew Smith with little or no trouble, especially after going by Andrew for a while. Even if you don't know, plenty of people you know are probably using a nickname or middle name. My uncle "Bill" was really named Charles, but nobody called him that after he was 12 or 13. The biggest issue there is probably dealing with a bank account. The bank may or may not let Hollingsworth Andrew Smith IV deposit a $50 check made out to Andrew Smith. I can safely promise they won't allow a deposit of millions.
Even if you can claim anonymously, the important thing is to stay under the radar after collecting the money. You can be named Bob Smith and be easy to find or you can be named Hollingsworth Wilberforce and be nearly impossible to find.