The 'OG' online map platform, MapQuest, says it won't change the name of Lake Ontario

It’s not that MapQuest won’t change it, it’s that the name hasn’t changed.

But Goog map added “Gulf of America” under the Gulf of Mexico while MapQuest retain the Gulf of Mexico, so even when it has changed for USA MapQuest basically saying they won’t follow.

Again, not that they won’t follow, it’s that the name hasn’t changed. Trump can do what he likes and he can probably force the executive branch to use the name in official documentation, but other than that this stunt means nothing

The name of something is not an inherent property of that thing. All names are assigned.