Brands are words that need to be trademarked, but "a cow" does not need to be, because everyone knows what a cow is, and if I sell you what I say is a cow but is actually a cat and then explain that that's now the established brand - you'd say it's cat, not a cow.
The test for Bitcoin is very simple - fire up an old version of the Bitcoin software, and if it validates the blockchain, then the blockchain you have is Bitcoin. If it doesn't, it's not Bitcoin.
And if/when Bitcoin Core ever changes the software such that it is a hard, backwards incompatible fork, then on that day they should stop referring to it as Bitcoin, because it is not the Bitcoin that Satoshi originally started.
