In the US the dollar has names for smaller amounts (like a quarter, a dime, a nickle, a penny).  Bitcoin needs something like this.  I propose that it be loosely based on the metric system.  As follows:

0.1 Bitcoin = deci + coin = deco (pronounced deck-o)
0.01 Bitcoin = centi + coin = ceco (pronounced sek-o)
0.001 Bitcoin = milli + coin = mico (pronounced mik-o)

Hope this helps