I think that the best way to give .001 bitcoins a name is to call it a bitmill.  People say abbreviate bitcoin as BTC, so similarly, a bitmill will be abbreviated as BTM.

One dime could be .1 BTC
but .09 bitcoins could be called 90 BTM or .09 BTC.

In a summery, people should name things as bitcoins or bitmills, no bitcents (since BTC could stand for bitcoin or bitcent).  Bitmills could be abbreviated as BTM.