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 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 up to the renderer what to display. OSM tags data according to global consensus, they use Gulf of Mexico for 'name'. There is an attribute for 'official_name:en-US' that returns Gulf of America. Same approach for other disputed names/places.

https://wiki.openstreetmap.org/wiki/Key:official_name:en-US

"Few if any renderers consume official_name=* or any of its subkeys; in practice, the purpose of this key is for geocoders to find the feature when a user searches for the official name."

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."

It’s interesting how the “preserve traditional historical names - don’t change the names on things for political reasons” role flipped to the left when that particular person started renaming things. In this case especially - a body of water that is between two countries has no “correct” namesake. It merely has a “traditional” name justified by “that’s just always what we’ve called it.” Tradition suddenly became very important to the American left wing when that rename happened.

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.

Hopefully not. Whatever changes Mr Trump demands will likely be temporary, regardless.