Cornwall-on-Hudson, NY
Shelter Island Heights, NY
Isn’t the capital said as Washington Dee Cee ? contracted spelling doesnt mean its not three words.
Or rather, the use of D.C. , Washington, Washington DC, means that “Washington District of Columbia” is in use… the sum of the parts… Its like the UK is also G.B. ,so " the UK of GB" is in use, as both halves are in fairly common usage.
I would argue that the name of the capital city (capital refers to the city, capitol to a building in it) is Washington, and that District of Columbia is the name of the federal district it is located in. Nowadays the two are coextensive because there is no city other than Washington in it (there used to be two others, Georgetown and Alexandria), but I’d say that linguistically there is still a distinction between the two.
Geneva-on-the-Lake, Ohio.
And the hyphens are part of the name.
I looked up the Seattle City charter. Four word name:
Section 1. - MUNICIPALITY; NAME, BASIC POWERS:
The municipal corporation, now existing and known as The City of Seattle, shall remain and continue a body politic and corporate in name and in fact, by the name “The City of Seattle,” and by that name shall have perpetual succession, may sue and defend in all matters and proceedings whatever, have and use a common seal, and alter the same at pleasure, and may purchase, receive, hold and enjoy real and personal property within and without its corporate limits, and may sell, convey, mortgage and dispose of the same for the common benefit, and may receive bequests, devices, gifts and donations of all kinds within and without the City for its own use and benefit, or in trust for charitable or other public purposes, and do all acts necessary to carry out the purposes of such gifts, bequests, devices and donations, with power to manage, sell, lease or otherwise dispose of the same. No gifts of munitions, military supplies, gas or police equipment shall be accepted by The City of Seattle without approval by ordinance.
San Luis Obispo, home of the Cal Poly SLO Mustangs. 
I don’t think that counts. The multiple-word constructs of the “City of X” sort that are used for the formal name for legal purposes are not what is in common usage.
From the OP. I guess I didn’t read carefully. Carry on.
Washington, D.C. - Wikipedia.
" Washington, D.C. , formally the District of Columbia"
Georgetown is technically a neighborhood near the University, not a city. Alexandria has always been in Virginia.
Georgtown was founded in 1751, 40 years before the District of Columbia was created. It remained a separate city within the District of Columbia until 1871, when the separate governments of the City of Washington, the City of Georgetown, and Washington Township were eliminated and merged into the single District of Columbia government.
Similarly, the City of Alexandria was a separate city within the District of Columbia from 1791 until retrocession of the Virginia portion of the District of Columbia in 1847.
It’s kind of a complicated situation. The City of Washington no longer exists as a chartered jurisdiction at all. It’s not that the City of Washington and the District of Columbia are co-extensive. It’s that as a legal jurisdiction, there is no City of Washington.
Thus, the capital city is Washington, D.C., but it is a city in a generic sense of a human-occupied conurbation, not a City in the sense of a formal legal jurisdiction.
This map makes it pretty clear. It helps to recall that the District was originally a square ten miles to a side, and that it contained land on both banks of the Potomac.
Schnitte wrote:
I would argue that the name of the capital city (capital refers to the city, capitol to a building in it) is Washington, and that District of Columbia is the name of the federal district it is located in. Nowadays the two are coextensive because there is no city other than Washington in it (there used to be two others, Georgetown and Alexandria), but I’d say that linguistically there is still a distinction between the two.
I’m told, by people who lived in DC a lot longer than I did, that until the late 1950s the District’s major neighborhoods east of Capitol Hill were effectively towns. Letters up through the Eisenhower administration were commonly addressed to Georgetown DC, Brookland DC, Shaw DC, etc. This was probably extra helpful to the Post Office, since the ZIP Codes didn’t happen until 1963.
DC didn’t have a mayor as such until 1974 (Walter Washington served as Mayor-Commissioner from '67-74, but most people just called him “Mayor.”), and that an appointed Governor, Commissioner, or Bord of Commissioners performed the tasks associated with the office prior to that. Old cemetery headstones in Alexandria actually say “Alexandria, DC.” Anyway, Washington didn’t quite reach all the boundaries of the District of Columbia until a lot later than you think.
That was the original plan. But then Virginia changed her mind and we ended up with this:
Retrocession is actually quite complex and it’s not all past history - District of Columbia retrocession - Wikipedia