We could be called America if we want but someone would have to propose a name change and it still wouldn't completely co-op the use of the word America to stop having it refer to this entire hemisphere. We all understand that Columbia is a country but Columbia is also a term to refer to this hemisphere which is why we have a place in the United States called Washington district of Columbia. No one confuses that as being a part of the nation of Columbia.
So in the terms of it being the Gulf of the Americas, It absolutely is it's not completely encompassed by one country. We as a nation need to stop calling ourselves Americans as an exclusionary term simply referring to United States citizens. All of us in this hemisphere are Americans but have a different nationalities.