The "White House” is (today) synonymous with the Capital of the United States and the home of the U.S. President. However, the very first Capital of the U.S. was in New York City and is where George Washington and family first lived after George Washington became President in 1789.
The U.S. Capital was relocated to Philadelphia, Pennsylvania, and occupied by George Washington & family in December 1790. It was referred to as the "President’s House”. The last U.S. President to occupy the "President’s House” in Phila was John Adams who was still President when he moved to the newly finished Capital building in Washington District of Columbia in November 1800.
At the time, the new Capital went by various names e.g. "President’s Palace”, "Presidential Mansion” or "President’s House”. The term "White House” first surfaced in 1811. There was an interruption in 1814 when British troops set it ablaze during the "War of 1812”. The "White House” was restored in 1817 when James Monroe was the first U.S. President to occupy it.
The name "White House” was not made official until President Theodore Roosevelt made it official by having "White House – Washington” printed on the "White House” stationary in 1901.