At the end of the day a map provider has the responsibility to show the official names of places on a map. If it’s one name to the US and another name for the rest of the world, the pragmatic solution is to show the “right” name based on a user’s location.
This seems like a silly hill to die on, when whoever is in office next will likely revert the names of the lake and the Gulf of Mexico, unless they are deep in the Trump camp.
Messing with maps as a negotiation tactic seems rather boneheaded. It’s extremely disruptive, but blaming Google or Apple for any of this is a bad move, imo. There are much bigger fights to be had and they need to pick their battles. This isn’t it, and it will likely resolve itself in time, and should only impact those in the US, if done right.