There's a whole list of examples here. I first learned of this in my high school Spanish class and it's been around in the back of my head for many years. Just occurred to me that I might be able to ask in this sub and actually get an answer :)
Essentially the answer is because we don't speak the language that they do. So most names of places are attempts to represent the sound of that name in the sounds and letters of English. In some cases they represent historical attempts to do that that have persisted, even when the name of the place has diverged/changed in other ways.
I am pretty sure this is in the faq. If you wanted to know about any particular city or place, feel free to follow up.
It's also worth noting that in modern times we often don't. For example, while Japan is an anglicized country name, its cities (Nagasaki, Tokyo, Toyokawa, etc.) are referred to by their Japanese names, even if they might be poorly pronounced. The same goes for Korea— that anglicized country name came from Marco Polo's 17th century approximation of what the Chinese were calling it at the time, where it spread into all those European languages, but we call all of their rivers and cities and mountains by their current Korean names.
China can be a slightly mixed bag— for example, the end of the Liaodong Peninsula used to be translated into all the European powers' languages as "Port Arthur" (Порт-Артур in Russian), named after a British officer during the Opium Wars, and the name persisted into the 20th century, but now we call it Lüshunkou.
Equally fun is seeing when there are Sinicized names for our cities in Chinese versus transliterations. Like, Boston in Mandarin is just Bōshìdùn, a clear approximation of Boston, but San Francisco is still called Jiùjīnshān, meaning Old Gold Mountain.
Some of them are changing back as well - particularly some less well-known places in Germany where for a while the French name was used in English. These days we say Aachen, Trier and Regensburg, not Aix-la-Chapelle, Treves and Ratisbon, for example, but "Cologne" for "Köln" is just too well ingrained.
Besides the other posters explaining that the English names are approximations, there's also the fact that names continue change in the source language as well as English. For example, when the name of the city of Paris came into English, the then French (or those who would become French) pronounced the S. English speakers didn't routinely check back with the French to attempt to reapproximate their new pronunciations.
I can try to find some sources on the pronunciation of Latin and Old French if I must.
For an in depth explanation of any particular cities (or of language in general), I'd recommend /r/linguistics. It's a great place and they have a weekly Q&A thread if you have any more language-related questions.
I'm putting it up here, too, because as this is a historical subreddit, you might get a better answer on one dedicated solely to languages.