Sadly, all that name changing back and forth for the lottery wouldn't work in my state -- New Mexico -- because the courts are notoriously slow to schedule and the Lottery Commission demands you claim within 90 days. And we're a non-anonymous state when claiming, although you can decline a picture and news conference (but your name and home town will be publicized.) Best to set up a claiming group, a representative claimer (financial attorney), a bridge trust and a receiving trust. But, still, at that size of a jackpot somebody will do the super sleuthing to try to figure out who you are. Don't blab to family or friends until you claim the jackpot. Otherwise you'll be inundated. And don't make new friends after you announce... You think they're really interested in you?
Most folks move after winning, mainly to try to resume a level of privacy. Everybody will claim a "need" for $50,000 or have some business venture you might be interested in and will hound you about investing. (Although at $1.6B I think you don't need to worry about making more money; right?) Develop a firm resolve to say "No" or, if you have problems with that, defer them to your financial advisor -- and you should have one and an attorney in your employ and on the payroll -- who under your orders will deflect.
Most advisors suggest just sitting on the jackpot for a while so you can figure out what YOU really want. It's okay to blow a small amount of the money, but invest the money. Put a parcel in a foundation effort that will distribute charitable interest to whatever you feel like donating to. Put another parcel of money in an account that you could live off the interest. Put a parcel into another interest-earning vehicle so you'll always have funds to live on. Take care of you first, then set up the family.
Above all, the lottery jackpot is meant to make your life EASIER and for you to enjoy life. So hire others to help you handle it -- tax advisor, financial advisor, attorney -- but at your wishes. So figure out a way to enjoy your windfall, even if it means getting way away on a regular basis.
But, yeah -- sorry -- you'll be a celebrity. And your life will never be the same. Let's hope it's in a good way!