Sure but you can leave some of those up to local nuances - like in Canada maybe they show both. In the US maybe they don't since we only call it the English Channel.

But I'd say that it's probably not a big deal anyway because how often are you going to run into such a scenario, and even if you do how would Google/whoever capture a lot of informal names for things? A little bit of confusion is fine too anyway.

At google scale I imagine at least millions of times per day if not more. For what it's worth, here in CA it's just "English Channel" and I like that. I'm just saying that I don't see a way to do it perfectly every time, I agree that a little bit of confusion is OK.