Well, when you visit it https://www.openstreetmap.org/#map=7/23.765/-87.100 there's no naming of that area at all. At least when looked at from a US IP. And when you search "Gulf of America" it returns "Gulf of Mexico". So take from that what you will.

Fiat never works for linguistic shifts. That order is about as likely to work as telling a kid to stop saying "six seven."

The President of the United Stated doesn’t actually have the authority to tell anyone besides the executive branch what to name geographic places. So the order will only forces official US government maps created by USGS and the like to be updated. Other maps can choose to update if they want to.

Open Street Map tends to reserve the “name” tag for what things are commonly called by the local community. It appears that for the Lake Ontario and The Gulf of Mexico they’ve added an “official_name:US” tag to capture the names in the executive orders.

It's community driven, so I highly doubt the public will change it.

Now, I'd love for each geographical region to take their very worst area, and rename it after a certain politician for the lulz.