Just use SI prefixes!
1BTC = 1 bitcoin
0.1BTC = 1dBTC = 1 decibitcoin
0.01BTC = 1cBTC = 1 centibitcoin...
The prefixes "deci" and "centi" are not SI prefixes. They are leftovers from the pre-SI metric system, and they add more complexity than benefit. So let's keep it simple...
1 BTC = 1 bitcoin
0.001 BTC = 1 mBTC = 1 millibitcoin (nickname "one Millie")
0.000001 BTC = 1 uBTC = 1 microbitcoin (nickname "one Mike")
The base unit of 0.00000001 BTC is the same as 10 nanobitcoins, but I think this will be confusing because we cannot represent 1 nanobitcoin (so how can we have ten of them?). The existing usage seems to work well enough:
0.00000001 BTC (nickname "one Satoshi").
That makes total sense. It's simple, it's easily converted (as most people are familiar with metric system) and the nicknames are totally usable.
As far as the last two digits go, I think the setup you have will work out fine as it is. In the same way most people would say $1.35 as "a dollar, thirty five" people could also say 1.28 uBTC (0.00000128) as "a mike, twenty eight". So a name for the last two digits isn't really necessary. As they are the last two digits, you could call them cents (mike-cents) if you really wanted to. The thing is though, years from now as we approach the point when we actually need a name for those digits, we'll also need a system that works further than 8 decimal points anyway. So before we ever need a common name for the last few digits, the system will already need to have been extended to include nanobitcoins, picobitcoins, etc. Technically, the furthest few digits in the system will never really need
a common usage name.