That is true
, though it is possible that maybe the City of Washington, where the popular prefix comes from, isn't named Washington; Perhaps when the Three Commissars inform Washington that the Federal City will be named after him, he humbly requests they do not out (Maybe Washington felt that naming the Capitol after him would give the impression that he was solely responsible for America). Columbia becomes the favored alternative, and the Capital is officially '
The District of Columbia', or '
Columbia' for short, and confusion regarding state and district is avoided.
An alternative would be the City is named after the Potomac river, or after Maryland (
Federal District of Maryland, though this would be after the retrocession and the most unlikely).
On the State, I have some alternatives:
-Vancouver (After the man, who first visited the area whilst charting the North West)
-Jefferson (Because founding fathers)
-Cascadia (After the mountains. Already mentioned, I just like it).
-Casylvania (Because puns)
-Duwam (Shortened version of Duwamish, the river and tribe near Seattle)
-Columbia (Most likely, although the reasons why they didn't go for it, as pointed by the OP, are amusing)
-Monsylvania (Means Mountain forest in Latin, I think. Obviously reflects the States Mountains and Forest)
-Tacoma/Rainier (after the mountain)
-Olympia (After the Capitol of the State)
-Washington II: The Wrath of Stanton
-Whale (After the shape)
The naming Committees for the District and State are honestly my favorite PoD's.