Another idea to give names basing on how many times you have to divide Bitcoin by 10:
1 Bitcoin = Bitcoin
1/10/10 = 0.01 Bitcoin = Dibit
1/10/10/10 = 0.001 Bitcoin = Tribit
Use greek prefixes mono, di, tri, tetra, penta, hexa, hepta, octa, nona, deca
I really like this one - it follows a set pattern and is easily memorable. Additionally, it means we won't have this debate every time a decimal point moves... Definitely my vote!