The endonym and exonym in English were the same previously (Gulf of Mexico). The endonym is now is changing to Gulf of America while the exonym is remaining Gulf of Mexico.
I'm not aware of any other places where there is the case in English but looking at places in India it seems the exonym just appears on a different line above the endonym.
I've come across similar reports about Google Maps before. The way maps are displayed can vary depending on the viewer's location. For example, if a country claims a particular territory as its own, citizens or residents of that country might see the map reflecting their government's claim. Meanwhile, people in neighboring countries or those opposed to the claim would see a different version of the map. I won’t mention specific examples, but this is how it generally works.
That seems a little like a typo, or a broken sentence, because it make no sense. (Google) Maps users will see their official local name, i.e. Mexican users will still see "Gulf of Mexico" (but in Spanish), but apparently anyone not using Google Maps will see both names... How can Google know that?
Based on local news, what they will actually do is have Maps display Gulf of Mexico for Mexican users, and Gulf of America for US users. Everyone else gets both.
Local, traditional name and the official name requested by the country embassy. For example at one point Birma changed it's name to Mjanma. It looks like this https://postimg.cc/zHYKb3DF
https://en.wikipedia.org/wiki/Endonym_and_exonym
Different groups can have different names for the same thing. For example, country names change depending on the language.