Even "Gulf of America" wouldn't be SO bad if people like me (non-US English speaker) can wean ourselves off the habit of referring to the US as "America". I'm going to start doing my bit.
>>People in Latin America rarely call the US "America", although often call people born in the USA "Americano".
As an American not from the US who lives in America but not in the US, the only Americans I have heard calling US citizens "Americans" are people who live in the US, be them US citizens or not. Many of them acquire a cuban accent, btw (florida effect)
The regular gentilice we use for US citizens is "gringo" I don't know the origin, but it is not used as an offence. Calling them "Americans" does sound odd and a little offensive, ironically!
Latin America has started long ago, by calling itself America, and calling the USA, well, the USA (Estados Unidos). Still a bit annoying to Mexico (Estados Unidos Mexicanos), of course.