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").