Personally, I'm giving the word "cash" a chance. I'm going to try using it in my everyday language, and see if I can start thinking about 0.000001 BCH as simply one "cash".
The more I think about it, the more I like it, because it matters what you call something. When you call something "cash", it becomes cash in your mind. And, in order to be interesting, bitcoin must be cash. In order to bank the unbanked, obviate central bankers, and bring about a financial renaissance, bitcoin must be cash.
So, for the next few weeks, I plan on making a conscious effort to use "cash" wherever I would have used "satoshis", or "BCH". A few simple examples:
Sending a transaction costs 0.01 cash per byte.
Posting a Memo typically costs 2 or 3 cash.
Buying a cup of coffee currently costs about 2000 cash.
Speaking of the price of a cup of coffee, another opportunity we have as we switch to using "cash" is to stop thinking about the price of BCH in terms of USD. If cash is to be a global ubiquitous currency, we should instead think of the price of USD in terms of cash. In other words, rather than thinking 1 BCH is currently 1450 dollars, a more effective way to think about it is that 690 cash is currently 1 dollar. This makes it easier to calculate the price of a cup of coffee (or anything) in your head.
A note about "bits": People have been trying to make "bits" stick for the past 5 years. In my opinion, it's not happening. "Bits" already means something specific in the context of computers (i.e. one "bit" is either a zero or a one). And in the context of finance, it simply sounds too similar to bitcoin itself - to the uninformed, it sounds like "bits" might just be shorthand for "bitcoin". "Cash" on the other hand has the benefit of being distinct from the name of the system.
I believe that we have a unique opportunity that has ironically been given to us by the block-size debate and the very existence of Bitcoin Cash: the opportunity to name our currency unit something that is so well-known and well-understood that every user will instantly know what it is and what it can do.