You can make too much of this. Countries regularly have different names for foreign or shared places. The "English Channel" is "La Manche", Cologne is Köln. Like the English language, it's pretty much down to "that's what I call it". If people continue to call it "Lake Ontario" that's what it will be.
It's a country's leader petulantly ordering their entire country to call a lake by a new name that wrongly implies it belongs to them, which it doesn't, in order to spite their main trading partner because they rejected a trade deal that would massively harm them.
https://en.wikipedia.org/wiki/List_of_politically_motivated_...