Not in the mind of a foreigner writing about the American city. You have to realize that people in various countries have different points of reference. Most foreigners don't even know about Washington as a state. None of them know about the "original" Washington in NC, which locals refer to as Little Washington.

Now here's a puzzle for you. We can call other countries and cities by our preferred English names, such as Germany, Hungary, Moskow, etc. But a number of years ago, we were told not to say or write Peking, but to say or write Beijing. I wonder, why does that rule applies to China, but no other country?