Does anyone know if and when Esri plans to update its ArcGIS Online basemaps to be in compliance with Donald Trump's Restoring Names That Honor American Greatness executive order?
This blog article covers the details of the implementation, and how users will see it (or not).
Here's a follow-up blog with additional information that may be useful.
Any organization can create and use a custom basemap gallery. And you can edit any basemap using the Vector Tile Style Editor to reflect your own cartographic preferences, including changing labels for the Gulf and the highest mountain in the U.S. (I might suggest "Gulf of Bern" and "Mount Bern" if you are going to do that).
An easier way if you don't want to see "Gulf of America" in your organization default basemaps is to simply set your organization region setting to World rather than United States. Same basemaps, different labels. Personally speaking, that is what I do.
Bern
The basemap you use in a web map will be referenced in the map. So if you had your organization settings set to "United States" you would see G of A. If you then switch your organization settings to "World" then the web map, and any apps it is used it, would still show G of A. Though new maps you author would show G of M.
Same is true for ArcGIS Pro projects.
If dual labeling is the goal, then personally I would create a custom basemap gallery for my organization and include both the United States and World (or other) versions of the basemap in that gallery, clearly name them as such, and then you can choose which you want when you author maps.