but you can rest assured that there is going to be a battle for the name bitcoin since branding sis so important nowadays.
i think it'll be pretty straightforward. if one chain dwindles to 20% or less then it's over and the victor will be bitcoin to everyone who uses it.
maybe there'll be some patent, copyright or trademark trolling from the loser. no one's gonna care.
If a fork, its more likely neither gives up and we have multiple chains as a result. Bitcoin's price will suffer and it will probably take years to straighten itself out. ETH is not a good example that people keep using. It was newer, smaller, and less known. The reason for their split was different as well. Apples and oranges.