Hello from the other Washington.
New Mexico, California, Arizona, did not exist in 1770s. Those were largely unexplored territories populated by Indians far to the West.
Thirteen original colonies were all in the north-east: Delaware, Pennsylvania, New Jersey, Georgia, Connecticut, Massachusetts, Maryland, South Carolina, New Hampshire, Virginia, New York, North Carolina, Rhode Island.
United States grew slowly over the next 180 years by purchasing or trading or warring for more territory to the West. The final two territories to gain statehood were Alaska and Hawaii in 1959.
The name is no coincidence. Washington State was named after George Washington. The state emerged from the northern part of the Oregon Territory of old, after the dispute between the UK and the US was settled in 1846. The settlers originally called the area the "Columbia". Naming the new territory after the first US president was a clever attempt to gain recognition by the US Congress. The residents wanted to gain statehood. Similarly, two counties in Washington were named Pierce and King, after the then US President and Vice President. (Today we'd call it sucking up, eh?) It must have worked because Washington gained statehood in 1889.
http://en.wikipedia.org/wiki/Washington
Random trivia: "George" is a small town in Washington. George, Washington, getit???