Bitcoin will become known as the biggest speculation fail in human history. And in that case it's best if BCH is simply known as "Cash" of the internet (with no ties to the collapsed ponzi).
Future generations might not even know what paper cash is nor means. For them "Cash" will be equal to cash.
Furthermore it seems we still focus too much on BTC instead of other projects like ETH and XMR (who do many things much better, but just haven't seen appreciation from the market). It's most important to know your future competitors.