Gulf of Mexico is the common name, used extensively by all types of people since the 17th century. The idea that this is a propaganda nickname is so absurd that I can only consider it a bold faced lie.

The Gulf of Mexico/America/etc. is not a creation of law, the Department of Defense is.

Far as I can tell that law has no real jurisdiction over that piece of geography. To steelman you stupid point... Only Americans should be calling it that lol.