Simply name it JioTV+. + here refers to streaming content. Streaming linear TV channels must be exclusive to JioFiber user so + is for other content and non Jio user. It sounds good too. The more you experiment and explore. The more you ruin an existing good thing.
They will then have to rebrand the existing JioTV+ App in Jio STBs. That app provides the following content for Jio STB users:
1) Aggregate content from all other apps in the Jio STB.
2) Live TV from all other apps in the Jio STB (Zee5, Sony Liv, Voot, etc,).
3) Live TV that is exclusive to Jio STB, which are not available through other apps (Star Vijay from Disney+ Hotstar app which is not available in the same app for Android TV, Jio Cricket Channels, Raj TV, Polimer, Polimer News, etc).
4) Content exclusive to Jio STB, like movies and shows from apps that are not available in Jio STB (Lionsgate Play, Universal+, etc,).
In addition to this, the JIO TV+ App has a hard-coded button in the Jio STB Remote Controls for easy access. This would add additional complexity in the decision making process when it comes to rebranding the Jio Cinema & Voot Apps in order to integrate their existing content into the existing Jio TV+ App.