I don't think you understand, the Reino de Mexico was where modern Estados Unidos Mexicanos is, and Spain ruled from Florida (a spanish name) to the Yucatan (part of the Reino de Mexico), there was no need for political ploy to claim shipping routes, as the islands possesed by the french are far away from the gulf. Spain used to own it and named it Gulf of Mexico. Who owns it now? Who owns the Persian gulf? Are you willing to change the Gulf of Mexico for the same reason some would change the Persian Gulf? Or different standards for different regions? It is a real pain in the ass to learn that a couple centuries ago whoever selled more maps gets to name a region, alas propaganda has always been a pain in the ass.