IIRC - The story goes that originally Washington State was going to be named Columbia, as the Columbia river denoted the Southern border. Canada was like "yeah, that makes sense, we'll name our province above the U.S. Columbia "British Columbia."

But then the people from the U.S. side were concerned that people would mix up the state of Columbia with the District of Columbia (D.C.). So they decided to ditch Columbia and go with Washington. But then for some reason I don't remember the District of Columbia started calling itself Washington District of Columbia, which became Washington D.C. Leaving the situation just as confusing as what the Washingtonians were trying to avoid in the first place. With Canada saying "Well damn, now we have an entire province named British Columbia that is neither British nor part of Columbia".