BT Sport

[Aplus1]

Just to add to the naming suggestions, cycling content would be branded as Warner Bros Discovery BT Eurosport GCN from now on right   
On a serious note, could we see the return of the British Eurosport name for the BT channels while the Eurosport channels retain the current name?

Difficult to do - Eurosport isn't a premium sports brand, and people who are paying for BT Sport need to keep feeling that they're receiving a premium service. 

Despite several attempts trying to make 'Eurosport' a thing in America, to limited effect, it feels like Discovery just don't have a brand of sufficient stature to house BT at the moment. They'd probably need something new that would work in every country of the world. Eurosport is probably not it. Discovery Sport is probably not it. HBO Sports? Possibly, but it might carry the wrong connotation (e.g. Pay-Per-View) in the UK for those with long memories. And whether the Discovery management would swallow their pride enough to spotlight a Warner brand is also hard to guess.

I can imagine Eurosport retaining its name, perhaps with a prestige tagline to illustrate that it is "part of the HBO Sports network" or similar, but I can't really imagine the Eurosport name taking the main stage. Could be wrong though.