What about the capitol city of Myanmar? Doesn’t the US still refuse to acknowledge the gov. (and associated name changes) as legit?
In that category, there’s also Chennai (Madras) and Kolkata (Calcutta), the first of which especially has become common in English.
American soldiers stationed in Germany usually refer to the city of Kaiserslautern as “K-town” (Kaiserslautern, by the way, is the largest U.S. population center outside the territory of the United States, according to Wikipedia). The Germany city of Eisenhüttenstadt (the youngest city in Germany, by the way) is often just called “Hütte”.
Kingston upon Hull is usually just called Hull, but that’s the name of the river.
Derry/Londonderry:
Silver Spring, Maryland is not a school district nor an incorporated city. It’s the fourth largest city in Maryland, yet it has no clear boundaries. It’s just a postal address. So it in effect has two names, Silver Spring and nothing:
Chipping Ongar is usually just called Ongar.
And Chipping Norton is usually called ‘Chippy’ by locals.
What about Köln - Cologne
Or there are the contentious names for the British Falkland Isles, which the Argies like to call Las Malvinas.
Aung San Suu Kyi still uses Burma and Rangoon. So does the BBC.
Quite apart from what Lord Feldon and Batistuta said, note that I said “considered as places”, which was intended to forestall just such an objection as you nevertheless made.
One shouldn’t say “Myanmar”, one should say “Mother and I”. 
But Chipping Sodbury is usually called “Sodding Chipbury.” 
There is a string of postal addresses along the main line (of the PRR) west of Philly that have no legal existence: Bala Kynwyd. Narberth, Ardmore, Haverford, Bryn Mawr,… that are politically mostly part of Upper Darby Township (Bryn Mawr actually straddles the county line). Confusingly, there is also a postal address called Upper Darby, also in the township. The names used in the postal address are what the locals (and everyone else) calls them.
Cologne is just the Anglicization of Koln, much like Munich:Munchen, Vienna:Wien, etc.
A better example would be Frankfurt am Main, which everybody just calls Frankfurt.
I know that a lot of cities in North and Couth America were founded by Spanish colonists or missionaries who gave the original settlements very long names.
The full name of Buenos Aires, Argentina is " Ciudad de la Santísima Trinidad y Puerto de Santa María de los Buenos Aires." (City of the holy Trinity and port of Holy Mary of the fair winds)
And the full name of Los Angeles, California is "“El Pueblo de Nuestra Señora la Reina de los Ángeles del Río de Porciúncula” (village of Our Lady the queen of angels of the Porciúncula River).
Nobody has used those full names in centuries, most likely.
I think many out-of-state tourists are surprised to visit Kitty Hawk and find that Kill Devil Hills is a separate town. They use Kitty Hawk to encompass both.
The capital of the Indian state of Kerala appers on maps by its full official name,
Thiruvananthapuram, but i commonly known, by Indians and outsiders alike, as Trivandrum,
A number of cities in Canada have been amalgamated into new urbanities, identified by entirely new names…
The larger ones include Saguenay, Quebec, formed in 2002 from Chicoutimi, Jonquiere and La Baie. Thunder Bay, Ontario, was formed in the 1960s from Fort William and Port Arthut.
In the Netherlands, The Hague, Den Haag, and s"Gravenhage are all names for the same city.
Austin is sometimes referred to as Waterloo. Also, if you ask about River City, most folks will know what you mean.
Well, we know you’ve got trouble there.
Conversely, the resort town near Machu Picchu is officially called Machupicchu, but everyone calls it Aguas Calientes to avoid confusion.