It was originally to be called Columbia, per the wishes of some Oregonians who thought it ought to be named after the Columbia River. Richard H. Stanton and Edward Stanly, two members of the House of Representatives, argued that Columbia would be confused with the District of Columbia, and so that state was instead called Washington.

Since the territory is the District of Columbia, and the city itself is Washington — at least, that's how they were originally named — the fear was that if a state/territory were to be named Columbia, and especially if there were to be a city in said state/territory were to be named Washington, there could be confusion about which Washington in which Columbia might be being referenced.

Basically, the hope was that it might dispel confusion, rather than create it. I have no idea why the names on the table were Columbia and Washington (after Columbus* and George Washington, obviously) rather than some other name that might have been less confusing.

Source: How Washington Territory Got Its Name

Warren J. Brier

The Pacific Northwest Quarterly

Vol. 51, No. 1 (Jan., 1960), pp. 13-15

*As a few posters have rightly pointed out, there are a few steps between Columbus and Columbia. I should have written that the names were derived from them, but do keep this in mind.