An alternative approach based on the Associated Press:
The Associated Press will refer to it by its original name while acknowledging the new name Trump has chosen. As a global news agency that disseminates news around the world, the AP must ensure that place names and geography are easily recognizable to all audiences.
In OSM, this might translate to name=Gulf of Mexico / Gulf of America (“Gulf of America” is displayed, although with less importance), or name=Gulf of Mexico + alt_name=Gulf of America (“Gulf of America” is searchable, but not displayed by default).
President Trump also signed an executive order to revert the name of North America’s tallest peak, Denali in Alaska, to Mount McKinley. Former President Barack Obama changed the official name to Denali in 2015 to reflect the traditions of Alaska Natives as well as the preference of many Alaska residents. Trump said in his executive order that he wanted to “restore the name of a great president, William McKinley, to Mount McKinley.” The Associated Press will use the official name change to Mount McKinley. The area lies solely in the United States and as president, Trump has the authority to change federal geographical names within the country.
Same logic as before. If the changed feature falls entirely under one country’s jurisdiction, the change on the map should be immediate. If it is a feature shared by multiple countries, then prefer a common name and avoid recentism until sufficient consensus emerges.