Wokipedia says that the Gulf of Mexico/America was referred to at some point by at least some people as the Golfo de Florida. Here’s the cited source with, in turn, some of its citations:
Here’s the section that seems to be the basis for Wikipedia’s “other explorers”:
This seems like a good bachelor’s thesis topic a history major! Separately, if the Gulf of Mexico v. Gulf of America dispute can’t be settled amicably, my vote is for Golfo de Florida!
Maybe the President would settle for “The Great Water Hazard”?