It is not possible to remain completely anonymous if you win the lottery. You will have to report your earnings, and you should instead be consulting with an attorney to help manage both the publicity (just deny requests for interviews) and the legal ramifications.
The author is a Maryland attorney; however no answer given on Avvo is intended as legal advice or intended to create an attorney-client relationship. Dan's expertise lies in the electronic entertainment (video game) industry, as well as complex internet law issues, electronic free speech, entertainment law, copyright and trademark law, and computer fraud. He primarily represents game developers and founders of emergent internet technologies.