There already is a naming scheme, it's just based on the same naming scheme as the metric system (which the whole English-speaking world uses, except the United States for some reason.)

m = milli = .001
μ = micro = .000001
n = nano = .000000001

The smallest division is the Satoshi which is 10 nano's (.00000001) if I'm not mistaken.

Are you saying these should all just be scaled up? So what used to be a milli would now be a Bitcoin and what used to be a micro would now be a milli, etc?

I wouldn't see any problem with doing that; it would be analogous to share-splitting a stock which happens all the time.