Kind of a waste of time. I get it's just a name, but there are more consequences for mapping and maritime travel. I'm fine with Greenland and Panama, but this just seems stupid.
Having been to the Panhandle for about 2 years of my life I just call it the Gulf. I don't think the name matters at all.
The coastline of US and Mexico are both about 1700 miles each, but the Mighty Mississippi is the main drain into the Gulf.
So Gulf of Murica!