The naming policy is generally quite sensible, although individual mappers sometimes do weird things (OpenStreetMap is sort of an anarchistic collective). As long as most English speaking people around Lake Ontario and the Gulf of Mexico use those names, the `name` and `name:en` tags will reflect that. Usually the way media like quality newspapers use such a name is a good bellwether, and the normal name stays as long as it is evidently in common use.

If in the future most Americans do end up saying 'Lake America', `name` could follow that too, and Lake Ontario would end up in `alt_name`.

Or perhaps Americans from the White House to the New York Times to the school curriculum will call it Lake America, but Canadians will stick with Lake Ontario. In that case the top-level local language `name` might end up as 'Lake America/Ontario' (combining all local languages and variants) and `name:en` (English in general, so America would be a minority there) and `name:en-CA` would say Lake Ontario, and `name:en-US` would say Lake America. Time will tell. OpenStreetMap adjusts accordingly.

For the official name there is simply a different tag (`official_name`, or in this case `official_name:en-US` because the lake borders more than one country). Having that available makes it possible to search for it by that name.