OpenStreetMap also needs to deal with this kind of thing. In this case, several people already tried to add it to the map in some form of other, but generally not as something to actually be shown. There is a looong discussion about it here https://community.openstreetmap.org/t/gulf-of-america-gulf-of-mexico/124571 . General opinion is that it is (or will be) “the official name that the US says it has”. In OSM you can invent tags for anything, so an object can have many names. Done like this, anyone using the data can still choose to give precedence to any “official US names that are not in common use yet”.
Later it may be upgraded ased on if it becomes a common alternative name, just in the US, or maybe beyond. All those options can have their own special tag. And only very motivated data users will ever show it to map users. But if you do a search for Gulf of America, you will be able to find it.
OpenStreetMap also needs to deal with this kind of thing. In this case, several people already tried to add it to the map in some form of other, but generally not as something to actually be shown. There is a looong discussion about it here https://community.openstreetmap.org/t/gulf-of-america-gulf-of-mexico/124571 . General opinion is that it is (or will be) “the official name that the US says it has”. In OSM you can invent tags for anything, so an object can have many names. Done like this, anyone using the data can still choose to give precedence to any “official US names that are not in common use yet”. Later it may be upgraded ased on if it becomes a common alternative name, just in the US, or maybe beyond. All those options can have their own special tag. And only very motivated data users will ever show it to map users. But if you do a search for Gulf of America, you will be able to find it.