Well since I happen to be a financial services representative, I would do it this way if I were to win a nice jackpot lottery prize:
1) Rent a PO box at the post office;
2) Establish a trust (with wording that does not reveal my last name) through my legal team
3) Once trust is established, go to lottery headquarters to represent my "client" as the financial representative.
4) "Client" (me) will provide a written statement that again will not reveal my identity.
This will allow me to conduct the required publicity while at the same time remaining anonymous as I will not speak as though I was the winner. If anyone points out that one of the beneficiaries happens to be me, all I need to say is I am a close friend of the trust family. End of story. But I would ask them to not reveal the names of the beneficiaries, so hopefully that would be a non-issue.
As for my post claim life, since I represent big money from time to time, my income goes up and down all the time, so I would be able to mask this win from the people I know for a long time (that's a clue for all you salaried folks).