Are there other instances of differing names by country? I don't mean language differences. I found it strange that for the rest of the world, they'll see both.
But this isn't a territory dispute this is just an internal US name change.
Here in the Czech Republic it now shows up as "Mexický záliv (Americký záliv)". Why are they adding "Americký záliv" in a parenthetical? It's not like the executive order has any effect outside the US. Why would they change the name in any way anywhere but in the US? By what reasoning would they change the name in the Czech Republic but not in Mexico? US official naming means nothing to Mexico just as it means nothing to Czech Republic.
https://en.wikipedia.org/wiki/Persian_Gulf_naming_dispute