This is a nice interpretation of it, and maybe if this sticks we can reinterpret it that way, but this is coming from the guy who coined MAGA, the title of the order is "RESTORING NAMES THAT HONOR AMERICAN GREATNESS", and the text makes it very clear that it's about the US:

> It is in the national interest to promote the extraordinary heritage of our Nation and ensure future generations of American citizens celebrate the legacy of our American heroes. ... in recognition of this flourishing economic resource and its critical importance to our Nation’s economy and its people, I am directing that it officially be renamed the Gulf of America.

I saw a "Gulf of the Americas" suggestion which makes the second-most sense, after not changing it at all.