The only way you can stay anonymous in California is to use a legal entity, but that is not guaranteed. I looked at your posting from a few months ago and this is some of the information I have:
No state tax on Lottery Winnings for residents or non-residents:
Non –multi state lottery - Florida
Mega-Millions States - California, New Jersey, Texas, and Washington
Powerball States - Delaware, New Hampshire, Pennsylvania, South Dakota, Tennessee, and US Virgin Islands
No state tax on Lottery Winnings for non-residents but state tax for residents:
Mega-Millions States - none Powerball States - Washington DC and West Virginia
State tax on Lottery Winnings for both non-residents and residents: Mega-Millions States – Illinois, Massachusetts, Maryland, Michigan, New York, and Virginia
Powerball States – Arizona, Colorado, Connecticut, Idaho, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Minnesota, Missouri, Montana, Nebraska, New Mexico,
North Carolina, North Dakota, Oklahoma, Oregon, Rhode Island, South Carolina, Vermont, and Wisconsin