I don’t see why people are so upset about this. Mexico is in the continent of North America. if they were trying to rename it to “Gulf of the United States” or something then that would be less reasonable.
America is an extremely common synonym for the USA, for better or worse. It's not convincing to imply that you believe a president of the USA, renowned for his nationalist rhetoric and pettiness, renamed a geographic feature bordering Mexico and the USA from "The X of Mexico" to "The X of America" not as a reference to the USA.
Regardless, it's antagonistic to the namesake for no good reason, no matter what the new name is.