You make a very good point.

The thing is, it can't be done justice to by a single monetary tier. In an advanced financial system the trading currency (units which measure the value of the trade) is abstracted away from the collateral that backs it.

If you want to actually use the collateral itself to exchange for the good or service you're buying then that would be barter.

In the case of cryptocurrencies like Bitcoin, they are unbacked electronic assets and so qualify as collateral. When it's deployed in a commercial role though, it does in fact have your name on it - just like your house.

Here's two examples:

1. When you want to trade it for other currencies on a commercial trading platform you enter into a contract with an exchange whereby the contract assigns ownership of a certain quantity of blockchain balance to a designated individual (you). That balance may be fixed or floating depending on the contract (i.e. your balance might be at a designated address or a non-designated one). You then proceed to trade all day long, each one of those trades being registered, tracked and identified as being you. Finally, when you're finished you withdraw funds to the lower monetary tier where owner and possessor are no-longer distinct entities. (i.e. the owner IS the possessor)

2. If you have a Bitcoin backed credit card, you can move funds into a blockchain address that the credit card company designates. They will then credit you with a "tier 2" monetary token that is tradable in trading currency units as opposed to blockchain units. Again - all your trades will be recorded, identified and tracked and if you get stuff stolen in that monetary tier you will have recourse to a third party to restore your balance.

What you can't do is stamp your name on a bearer token - because then it would no longer qualify as such and consequently not qualify as bottom-tier collateral. (Because you need a third party to endorse the ownership). You COULD however enter into a barter trade with a bearer token because the mere fact that you hold it - means that you own it.

Put another way, potatoes don't grow out of the ground with anyone's name on them. Diamonds don't, coal doesn't and gold nuggets don't.

Thats the asset class that cryptocurrencies belong to. Like the potato, the diamond and the nugget that emerge from the earth, a crypto coin emerges from mathematical solution space....with nobody's name on it  

REF: A good reference on monetary tiers in the fiat system is the Bank of England website. Here you can see how one tier backs another and how successive layers become more articulate in terms of their monetary priorities but further away from the collateral that backs them as well as less liquid. The BofE has about 5 tiers, (only 3 of which are in use I think). They are named M0...M4

Base money supply tier:
http://www.bankofengland.co.uk/statistics/Pages/iadb/notesiadb/m0.aspx

M4 (Broad money supply) tier"
http://www.bankofengland.co.uk/statistics/Pages/iadb/notesiadb/m4.aspx