What's wrong with calling the gulf, Gulf of America?

What's wrong with calling the gulf, Gulf of America?

It's bordering two countries, wouldn't it make more sense to name it after the continent rather than one individual country? North America? The country is called the United States of America. I understand that most if not all people call it the US/America/the States/etc. I'd see the issue if it were changed to gulf of the USA, but I feel america is a general term? Though connotatively "America" is associated with the states.

To me it just feels no different than the Mediterranean Sea.