Eurosport and BT Sport to join together

[Transmission]

I doubt it, Eurosport is seen as a non-premium brand in the UK, on the basic tier of subscriptions. I can't imagine it'll be used.

BT Sport ESPN = ESPN by Eurosport, or Eurosport America (focusing on American sport)

The ESPN name will be gone from the channel imminently, anyway (as will "Extra", as it happens).

I have no idea what they'll do, but if I had to guess this is what I would speculate might happen: 

I expect they won't want to commit to a new name until they have decided how they are going to merge Discovery+ and HBO Max in terms of branding