One thing that does seem to be incorrect is that Google has a single name on the lake - Lake America, when surely that only applies to the American half. The US-Canadian border runs down the middle of the lake, so unless I'm missing something Trump's renaming only applies to the American half, and the correct way for Google to show it would be with different names for each half of the lake.

That's ridiculous! How do you rename half of a lake!

I say that there are two lakes. It remains for future generations to decide how the two lakes are apportioned. Perhaps each of them are coterminous, with the same boundaries, size and volume, but one is named "Lake America" and one is not. One is a lake in US waters, and the other is in some foreign country.

Perhaps of the two lakes, they are split in twain, and there is an international border running through the middle of these two distinct bodies of water. Perhaps vessels will littorally obtain right of passage in international waters, and undergo customs inspections before they can cross over the somewhat amorphous border between Lake Ontario and Lake America, and vice versa.