At various times in the history of the USA, the White House was known as either the "President's Palace," the "President's House," or the "Executive Mansion". It was President Theodore Roosevelt who officially gave the White House its current name in 1901.

It had been a popular myth in the 19th century that the White House was first painted white to cover the scorch marks left after the British Army set fire to the mansion in the War of 1812. Actually, to protect the exterior stone from moisture and cracking during winter freezes, the White House got its first lime-based whitewash in 1798. The term “White House” was in fact used before the War of 1812; the phrase appear in newspapers during the first decade of the 19th century.

In 1901, President Roosevelt made it official. What was then being called the Executive Mansion was formally named the “White House”. Because nearly every U.S. state had an “executive mansion” for its governor, President Roosevelt publicly stated that the name “White House” would distinguish it as the official residence of the President of the United States of America.

More Info: georgewbush-whitehouse.archives.gov