It's anonymous in the sense that you can create a different identity ID, but as soon as that ID is correlated to Domino's transaction # for that transaction, or any other slip of personally-identifying info, then you're no longer anonymous.
It's worse than That as you need to fund any new ID from another act. You can mine bitcoins and send them to a new act but the ip's used to generate those bitcoins are public.
Really for most mid sized transactions cash if far better, and dominos accepts cash unlike say amazon.com.
> You can mine bitcoins and send them to a new act but the ip's used to generate those bitcoins are public.
What? There seems to be lots of misinformation here. Please prove your point. There is no need to publish your IP when you mine. Most people mine in pools, and I guess the mining pool announces the block. But you can announce it through Tor, or you can solo-mine through tor.