There is no general rule. As Azelor ans kirkspencer said, place names tend to simplify overtime, loosing some vowels or altering/shortening the ending syllable, but this is true even without migration of populations or invasions :Suffixes -caster and -chester come from old English ceaster, itself from Latin castrum, sometimes through old French castre, the latine termination disappearing overtime. The name of Lannion (North Brittany) has slowly evolved from celtic Lann Huon (or Yuzon) without major change of population in this area.
Some thoughts :
- A city or place can be simply renamed and/or completly altered. Constantinopolis was built on the site of Bizance and has many other names by other nations (https://en.wikipedia.org/wiki/Names_...ther_languages) Constantinople inhabitants themselves named their city "stim boli" (in the city), which gave later Istanbul...
- All phonemes are not used in every language. For example, from my experience "v" is not used by japanese speaking people and they tend to pronce it "b", "l" and "r" are not distinguished and usually written "r", so imagine a world where Japan had invaded Europe, London would probably written "Rondon" and Venice "Benice" or something like that. You could play with this.
- A place can have kept is original name but its pronunciation been altered by new rulers : "Sai Gon" whas Frenchified as "Ségon" for a time.
- Language and culture shock can lead to misunderstanding and full of placenames are pleonasms and tautologies, arising from the mixing or juxtaposition of natives names and "invaders" language. In France "Mont Ventoux" (well known by cycling enthusiasts) come certainly from pre-latin root Vin- (height) and -tur (distance), which gives "Mont of the mont which can be seen from a distance". In "Chateaudun" -dun is a celtic root meaning "height, fort", that gives "Fortress Castle". There are many examples in islands and rivers names, too : -ey is a Saxon suffix for "island", so about all "(something)ey isle" are pleonasms in nothwest of Europe. Often conquerors simply added the field/place type (river, mount, coast, etc.) to a native name which already included that type, Mississippi (big river) river for example.
This reminds me a novel of Terry Pratchett where exploraters pointed the finger at a landmark and asked natives "what is this ?", who responded in their native language "I don't know", "What ?" or "Your finger idiot", these responses being promptly recorder on official maps. This certainly hapened in real life...