Is the change applied internationally or in the US only? Google Maps does have the capability to show a different name based on the user’s region. Since the official name is still Gulf of Mexico in the rest of the world, it would make sense to use the new name in the US only.
As long as it is not the "Gulf of the United States of America", I think it is still geographically correct. As long as my map stays with "Gulf of Mexico" on it, of course ;-)
Here in Germany, naming of places, roads, whatever is a constant debate. This is a very political subject, this is part of the public life of countries/communities.