In 1851-52 people living in Oregon Territory but north of the Columbia River petitioned Congress to make a new territory north of the river. They suggested calling it "Columbia Territory". The region had long been known as the Columbia District or Department of the Hudson's Bay Company (this is also why the Canadian province to the north is British Columbia).

In 1853 a bill was introduced in Congress to create Columbia Territory. Representative Richard H. Stanton of Kentucky amended the bill to have "Columbia" replaced with "Washington", saying:

...as we already have a territory [District] of Columbia...but we have never yet dignified a territory with the name of Washington.

The bill was passed by the House within five minutes, and soon after by the Senate, and signed into law by President Fillmore. As far as I know there was no other debate over the name at that time, and no serious debate over changing the name afterward.

It's always seemed funny to me that in order to avoid a conflict with the name Washington, District of Columbia, they changed the new territory's name from Columbia to Washington.

As if to illustrate the confusion they made worse rather than better with the name change: In 1863 the size of Washington Territory was reduced to make room for Idaho Territory. Idaho Territory was divided from Washington Territory by the meridian extending north from the confluence of the Clearwater and Snake Rivers, but the rest of Idaho's north-south boundaries were defined by "Washington meridians"—the 27th and 33rd Washington meridians. Were these meridians made for Washington Territory? No. Between about 1850 and 1885 or so territorial meridians in the US were defined based on a prime meridian in Washington, District of Columbia. ...maybe they should have called them "Columbia Meridians". You know, to avoid confusion?

Sources:

• Washington State Place Names, James E. Phillips, University of Washington Press, 1971.

• American Boundaries, Bill Hubbard Jr., University of Chicago Press, 2009.

• Idaho Organic Act 1863 – An Act to provide a temporary Government for the Territory of Idaho

• Settlers met at Monticello to sign a petition asking Congress to create a separate territory north of the Columbia River