With the giant continental shelves it’s not as if it’s separate from the nations bordering it. So what the US calls it is relevant, as is what Mexico calls it,

With the giant continental shelves it’s not as if it’s separate from the nations bordering it. So what the US calls it is relevant, as is what Mexico calls it, and Cuba, though that might be a side note. As a USian I strongly believe we should be calling it Gulf of Mexico FWIW.