One famous example in such respect is the name of Pakistan, which however was coined purposedly when it became an independent nation. It comes from an acronym formed from the names of the five northern provinces of the British India:
Punjab, Afghan Province, Kashmir, Sind, and Baluchistan (see here). The i vowel was inserted for euphonic purposes. However, the word paki has also a separate meaning in Urdu (where it means 'pure').
Another such artificial creation is the name of Banzare Coast, coming from British-Australian-New Zealand Antarctic Research Expedition that discovered it (see here).
You probably prefer some natural developments rather than an artificial creation. I am sure there are many examples. I can mention two Russian cities. First is Saint Petersburg which is commonly known, and effectively called, Piter by the native speakers. Someone calls it by the acronym SPb, even if more in writing than orally. Another example is the city of Yekaterinburg which is commonly abbreviated into Ye-burg, including also the spoken language.
The city names in the Spanish domains in South America were often derived from quite lengthy phrases with some religious content. Later they underwent spontaneous abbreviation. This is the case of Buenos Aires coming from the former denomination Puerto de Nuestra Señora Santa María del Buen Ayre (at least, according to the popular sources)
P.S. I suppose I don't need to mention Frisco for San Francisco.