Unpopular reality check:

Most people in real life just call it Apple TV. They know what they mean. "The Apple one".

Renaming the service to Apple TV is cleaner, and totally a non-issue. Only nerds obsess about naming these things. Nobody in real life will ever say the sentence "The TV app for Apple TV on Apple TV". Only people here do.

@viticci Pretty much this. Everybody I know just says, "It's on Apple TV." The celebrities who promote their shows on late-night talk shows say, "It's on Apple TV." Nobody is confused by this. We're all already doing it.
@ddribeiro I don’t even know anyone who says the plus. Even among the nerds I know with whom I talk about TV shows. I certainly never say it. They don’t even have a regular « Apple TV » service anyway. Everybody added a Plus to everything, to the extent of becoming a joke on The Morning Show. They should just get rid of all the Plus signs except maybe News+ as there is a free tier News. At this point it’s as weird as when there was no regular HomePod, just a HomePod mini.