You can't transfer ownership of the domain in your fork without either changing the rules—in which case it won't be accepted as a valid Ethereum blockchain by a

You can't transfer ownership of the domain in your fork without either changing the rules—in which case it won't be accepted as a valid Ethereum blockchain by any other Ethereum node—or else rewinding the blockchain back to a point before the domain was first claimed by anyone and starting over. In the end your private fork is pointless unless visitors to the domain actually refer to it as a source of information about the domain. Transferring the domain from the current owner in a way other nodes will accept requires private keys you don't have. Rewinding the blockchain means that your fork is much shorter than the first fork and has a lower cumulative proof of work, so other nodes following the consensus-based rules of the Ethereum blockchain will ignore it.