That would apply equally well to other bodies of water with disputed names, which have been stylized as e.g. Persian Gulf (Arabian Gulf) and Sea of Japan (East Sea) on Google Maps for like, 15 years?
well, there sure was a lot in the countries involved!! they have all lobbied and argued extensively in favor of their selected name for many years, and their people do seem to feel strongly about these matters.
I don't have a final answer for all situations, but certainly if you look at those things on the map right now they read one name, then the other in parentheses. The "Gulf of America" has no such parenthetical. That seems like an acceptable compromise that Google has already adopted in other disputes. I suspect it will rile the current administration, however, if they do so here, and so they have not.
edit: oh, I find Google has already addressed this, and it is only in the US that it is just gulf of america:
How much outrage have you seen over those names?