I dont think thats true.
Well, I don’t know the exact law, but if one could claim the grand prizes anonymously, the potential for fraud by government and lottery officials would be massive. Knowing the propensity towards human beings to steal when a large enough prize presented itself, this guy would never have won a prize this massive because some beaureacrat would have stolen it and remained anonymous. In fact, that is probably what would happen every week.
Also, I do believe winners have to agree to have their names and likenesses used in advertising for said contest in order to claim their prize. But I could be mistaken...JFK