I don't know for sure, but I'm almost positive that any bank would immediately turn you away for asking. I don't think there's anything illegal about it but the bank just really isn't for this type of thing. I'm sure they'll be happy to inform you that they'll waive the membership fee for their special checking/saving account if you put your money in their bank, though.
If you "sell" your ticket to any entity you will no longer be in control of the ticket as their name will have to be on it (especially since you want anonymity). You'd have to make some sort of legal contract with them which would require getting it notarized most likely. Also whenever they pay out to you (if everything up to that point works out) then you may have to pay additional taxes other than the original taxes, since YOU aren't the winner getting the money but rather an additional person getting paid. And remember, that's only if said contract could hold up in court, if not then you'd be out everything and there wouldn't be anything you could do. You'd likely want to hire a lawyer/attorney to be on your side and guarantee everything is safe.
I don't think any route would get you past having to report it to the IRS, as I'm sure every legit entity you "sold" the ticket to would report it to the IRS themselves. Unless you go the route of a random guy you have faith that they'll actually give you the money, and even then issues with the IRS may come up in which case they could eventually find out and you'd be charged with a possible felony.
My tip would be to either find a way to play in a state that allows anonymous claims or to collect winnings via a trust. For the second option any reputable person who can set one up should be able to do it in the correct way for this situation. I believe they can do it so that you are not the owner, but a beneficiary and all people will be able to find out about whichever trust won would be the owner/president which would be your lawyer/attorney/someone else not you. If you think about how often in the past people have claimed via a trust/LLC, you really don't ever know anything else about that jackpot winner in the future unless they come forward publicly to say they've won.
If you can't get to a state that lets you claim anonymously (you may be able to play online from one, not sure) and your current state doesn't let people claim through a trust... I don't know anyting else other than to say you could go through the process of changing your name and showing up to claim wearing a (modest) costume so nobody will know what you actually look like.
That's all the 'bored at night' advice I have.