The name “change” hasn’t even been adopted by the United States own government, because the president does not have that authority. Congress granted that authority to the US Board of Geographic Names in 1890. I suppose Congress could rename it if they passed a bill that the president signed into law overriding that authority for that specific case, but until they did so, it’s not official.

Here is the link to the US Geographic Names Information system page showing the current official name of the Gulf of Mexico: https://edits.nationalmap.gov/apps/gaz-domestic/public/search/names/558730. Note the list of accepted variant names, which still doesn’t include “Gulf of America”.

I just checked there, and they have not renamed it, nor have they listed the new name as a recognized alternate name.

Whether of not an executive order can override the government agency specifically granted that authority by congress is of no concern to them. By law, the Board of Geographic Names is the final authority on geographic names. If they don’t go along with this change, then the Trump admin would have to file an inter-government lawsuit about it.