How about...
Bitcoin ?
Using names other than Bitcoin - Andresen, Millibit, Satoshi etc will just confuse people.
Instead, redenominate the Bitcoin as 0.0001 BTC and rename the present Bitcoin a Satoshi.
So you will have
1.0 BTC old Bitcoins = 1 Satoshi.
0.0001 BTC old Bitcoins = 1 (new) Bitcoin
Yeah, that won't confuse people, I'm sure...
I don't think Satoshi is the ideal name, it's meant as an example.
Better to use something with "bit" in the name, since that can be regarded as the brand identifier for Bitcoin.
Also better for the names to be two syllable maximum since its easier and quicker to pronounce.
Anything longer tends to get abbreviated or cut down and given a shorter nickname by people and you then end up with something different to what was originally intended.
Important thing is to keep it simple.
Look at the Euro. When they were brainstorming names people came up with the idea of calling it something with "euro" in it. So they started out thinking in terms of calling it something like EuroFranc, EuroMark even EuroDollar etc. And even more complex combinations, some using Latin words, and trying to make the name sound profound.
In the event they just settled for Euro - 2 syllables, quick, snappy, everyone happy... except the Greeks ;-)
How about just "Bitcoin" and "Bit"?
You could then keep the present 1 BTC = 1 Bitcoin, and call the 0.0001 BTC = 1 Bit.
The currency code could be BIT. So 10,000 BIT = 1 BTC.
A "bit" is also a digital term, but it doesn't crop up in most daily conversation, so little chance of confusion. Can't get more simple than that.
What do people think? Bitcoin and Bit could get my vote!