The part of bitcoin that is anonymous is that, in most cases, a bitcoin address can not be attributed to a name unless its published.
In this respect, it is as anonymous as this board. All I would have to do to get a 'new identity' is reset my modem and make a new account (in this metaphor, hitting the 'new address' button).
sad to disappointing you, but...
have you ever heard of tracking cookies
I'm sorry to disappoint you, but have you heard of metaphors?
It's an example, not how it should be done.
And what about the 10,000 live CDs I have? I can easily reboot into one of those.