BT TV was rebranded EE TV as part of the proposed migration of all domestic BT Broadband customers to EE, thereby establishing EE as the consumer brand and running the BT brand for businesses only.
However, following a change in senior management at BT a couple of years ago, that plan was scrapped and the migration programme halted. The decision was taken to continue with both brands as a consumer offering, partly based on customer feedback regarding brand identity.
So the renaming of EE TV to BT TV for BT Broadband customers only is just the next stage in that strategy to make things more consistent for BT Broadband customers. That's all.
Yes, you could argue they have an identity problem, but we've seen the same things happen in other industries - just think RBS and NatWest, for example.
