No. We really don't.
If there is a fork, then one or the other of the two chains dies within a day. Whatever is left is BTC.
That was the case in with the previous forks where we had almost 100% consensus before the chain was forked. We now have two people and some followers that try to force the majority to accept their change package. Several people and some pools will not switch to the BXT forkcoin or use both coins BTC and BXT. There are good chances that we will continue with two chains. If this is established as a good way to push changes into the market, we might see several additional chains in the future.
This is fine with me. Everybody and every group of people is free to use their own set of consensus rules and fork the coin. But as long as the original coin is alive the forkcoin should not use the name of the original coin.