Bitcoin is a set of essential concepts, not a chain. No person can control the concepts. People will use it to describe one or more chains and splits as they evolve. This happens with all monies, including gold and oil which trade at different purities and qualities.
This is consistent with the declaration of Bitcoin, as it binds a set of concepts, not a set of rules, protocols, or implementations. People with capital invested have an inherent desire for brand association, but there is no such thing as a "legitimate" claim to it.