This was her nickname because she wasn't married. Actually, a lot of the states are named after royalty.
The Carolinas (North and South) are named after King Charles I of England. Maryland was named after Henrietta Maria, the Queen of England and Charles' wife. Louisiana is named after King Louis XIV of France. Georgia was named after King George II. Coincidentally, the namesake of the state of Georgia was the grandfather of the same George III that the colonists (including the Georgians) revolted against in the American Revolution.
With so many states named after kings and queens, it seems kind of strange that Washington is the only state named after a President.
A complete list of the origins of states' names here.