I don't honestly see a big issue with this. First of all: It's called Gulf of America, not Gulf of USA. Considering it's a gulf between south and north American continents it's actually a more fitting name and in no way excludes Mexico.
And secondly, you can just move on with your life and keep calling it the Gulf of Mexico and everyone will perfectly understand what you mean. Nobody is holding a gun to your head and telling you to adopt the new name. Same applies to Twitter and Facebook too for example.