I suggest SecureBits or something similar.
For me, Security is above all what I'm looking for.
Secure in my privacy : anonymity is a must
Secure in my transactions : transaction fidelity is provable
Secure in my trust : distributed participation that precludes centralization of control
With the above platform, what am I not safeguarded against? Sure, market demand may drive the value of the above currency to zero, but that has no bearing on the fact the infrastructure is worthy of use; is Secured.
The choice of the word bits isn't necessarily as copy-cat as it might sound either. A bit is intrinsically a piece of something. They can be added to together or broken down further. A bit has been commonly used as a currency valuing term in various places across the world and is already a part of many people's lexicon. Obviously there is the technical usage in the computer world. I think in the end it works on lots of levels and can be pretty accessible to a wide audience be they lay or technical.
I know liberty was mentioned earlier, but I think liberty is only truly held after it has been secured and true liberty is simply the guarantee of being able to succeed or fail without undue external pressure. That works on the market side of this coin, but I really don't like that meaning associated with the infrastructure. It could just be me, but I would rather have a term that feels more like a an obstacle overcome, beaten and well, secured, than one that means I now have the opportunity to fight the battle to the best of my ability. I don't think Liberty is as much achieved as it is lived in.
(edit: I kinda like the sound of SecureBlox too. A Blox/Block is made of 'something', it has a perceived value, it is still associable with the tangible world yet isn't necessarily defined)