The fort has seen several name changes. It started off in 1625 as Fort Amsterdam - protecting the original Dutch settlement of New Amsterdam. Since then it's been known as Fort James and Fort William, before changing sex to Fort Anne, and swapping back in the 18th century, to Fort George.
When the Revolutionary War ended Fort George was torn down (perhaps predictably, given that this latest name was in honor of the King).
Should really have stuck with Fort Anne. Everybody loves an Anne.