I was hoping that "someone" would respond (grin). I think you and I are probably in the minority - people who really WANT to retain their privacy and anonimity. A few months back, I put up a website with the results of extensive research on that topic:
http://LuckyYou.atspace.com
Here's an example. Kansas lottery law has a specific provision that mandates anonimity for all lottery jackpot winners. It's even an "exclusion" under Kansas state open-records laws. The ONLY way they can release a winner's name to the media is upon "written" request of the winner.
You'd think that with a law like that, and assuming the winner didn't spill the beans himself/herself, their anonimity would be assured. Not necessarily. If there's an unclaimed jackpot, media entities sometimes send stringer reporters to wait in the lottery commission lobby - to take photos of winners who show up in person - and later track them down to their homes by watching them drive off (and taking note of their license plate number - running it against motor vehicle records).
But, even if you redeemed your ticket by registered mail, there's still one way a winner's identity could become public. Here's a true story shared with me by one lottery official about a guy who wanted to keep his identity secret, had the laws on his side, but still couldn't keep it secret.
Retailers selling lottery tickets get a "bonus" for selling jackpot winners. After the drawing, one retailer was notified he'd sold the winning ticket - which includes telling the retailer the ID number of the ticket. Using his lottery terminal, the retailer pulled up info on the ticket's ID number showing the date and time the ticket was sold. Then, going through his store's surveillance video archives until he got to that date and time, he saw the winner buying his ticket. And the next time the winner came into the store, the retailer recognized him and congratulated him in front of other patrons - some of whom knew the winner personally.