In Medieval Europe it was also a case of many centuries passing, multiple conquerors and languages moving in and changing names that way. There was simply a longer period of time for placenames to diverge in Europe than in the Americas. That being said, quite a bit of place-name corruption in the Americas has occurred already since the colonial era.
Remember that European settlers of the Americas also mispronounced the native names which in many cases led to the current names.
e.g. The Wôpanâak (Wampanoag) word Masach8sut (Muhswatchuiset) became the English word Misswadchueeset, which became Massachusett, which became Massachusetts.
Names from other European languages were also modified. One example is English pronunciations of cities, states, and rivers from Spanish names. For Los Angeles, every vowel in the English pronunciation /las 'ændʒələs/ is different from the Spanish pronunciation /los 'anxeles/.
Also, if English was universally spelled phonetically, and the spellings of city names were changed to reflect the local pronunciation, a lot of cities and states in the U.S. especially eastern U.S. would be as distant from their original names as some of the cities in Western Europe. The conservative and irregular spelling of English conceals many of the pronunciation changes that have happened.