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 Yes, they already do call it that. That's the problem, they're different things, they should have different names.
Witness my parents who just bought three new TVs because they wanted to watch something on youtube, so they needed a TV with youtube on it. They couldn't use the AppleTV box because the show is not on AppleTV (the service).
We need to be pedantic, because it's the right thing to do, for clarity.
Federico Viticci 
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