Maybe as penny is to cent we need a satoshi to....?
Well 1 penny = 1 cent, so maybe dime/quarter is to cent is a more fitting way to describe what you're looking for? I do get where you're coming from though. As Bitcoin became pretty much unsuitable as a base unit, people started using mBTC, which currently cost around $10 each. It's also likely to become unsuitable itself in the future at which point uBTC is likely to be used next, but it's only 2 decimal places away from sats; do we really need something else between those?
I also get the merit of shifting to satoshi-centric units from BTC-centric units, but since hectoshis already exist as uBTC (which is much more well known) it could just add to the confusion.