George Washington's Birthday is celebrated as a federal holiday on the third Monday in February. It is one of eleven permanent holidays established by Congress.
Federal holidays apply only to the federal government and the District of Columbia; Congress has never declared a national holiday binding in all states and each state decides its own legal holidays.
Contrary to popular belief, neither Congress nor the President has ever stipulated that the name of the holiday observed as Washington's Birthday be changed to "President's Day."
Of course...state governments, schools, or the company you work for, can call a holiday whatever they want to call it. They can also declare the holiday celebrates whatever they want it to celebrate. But the Federal Holiday that is today is only for George Washington.
Ironically...Washington was born on February 11, 1731 (while the Julian calendar was still in use.) This became February 22nd, 1732 when we switched to the Gregorian Calendar. The earliest the Third Monday of February can fall is February 15th. The latest it can fall is February 21. It is impossible for the Federal Holiday "Washington's Birthday" to be celebrated on Washington's real birthday, according to either the Julian or Gregorian calendar.