For instance, Rome is spelled "Roma" in Italian. English speakers call the city "Rome" to make it sound more English. Another example is the city of Moscow in Russia. In Russian, the city is pronounced like "Moskva". Still, English speakers call the city "Moscow" because it is easier to say.
Most of these changes were made a few centuries ago. In some cases the original language was different to the modern one. Turin in the Piedmont province of Italy was called Turin in the original Piedmontese language, but is now officially known as Torino in Italian. The English and French name for Florence in Italy is closer to the original name in Latin (Florentia) than is the modern Italian name (Firenze).
Anglicization has a political/cultural dimension. All Welsh and Scottish Gaelic names were anglicized. Now they have their own local parliaments, they changed the official names back again. In Scotland few people speak Gaelic, so in practice the English versions are almost always used. In Wales all road signs need to be in both languages.