If the idea is to map it as a legal fiction, then it would have some primary feature tag other than place=sea and there would no longer be a reason not to use name=*.
Agreed. What the U.S. government said they mean is:
The Gulf of America, formerly known as the Gulf of Mexico […] is a major body of water bordered and nearly landlocked by North America with the Gulf’s eastern, northern, and northwestern shores in the U.S. and its southwestern and southern shores in Mexico. Bordered by Cuba on the SE, it connects to the Atlantic Ocean via the Florida Straits between the U.S. and Cuba, and the Caribbean Sea via the Yucatan Channel between Mexico and Cuba.
The extended continental shelf does not extend to the Yucatan Channel or southern shores in Mexico. The GNIS entry still gives Gulf of Mexico as a variant name.
GNS has only a single feature (ID -1506402) situated where we have the existing gulf node, bearing Gulf of America as the “conventional” name and Gulf of Mexico as the “variant” name.
The National Map, USGS earthquake maps, FAA aeronautical charts, and more have all been updated, none of them distinguishing the continental shelf as a separate body of water.
None of this necessarily means any other country recognizes these claims, any more than Mexico must recognize the U.S. federal government’s name for the Sea of Cortés or Japan must recognize the Virginia state government’s name for the Sea of Japan. None of this necessarily means we should do anything but acknowledge that someone out there thinks something is a certain way.