Agree that cc transactions can't be really anonymous, but if (and when) we are not storing the card information on the server and tell that to customer, I think what Russell says is as anonymous as it gets with the current infrastructure. Dunno what's going to be on our account listing, though, since I've never received a cc payment, but I'd think the name is not there :)
Of course there's emerging technologies that make real anonymous payment methods in internet possible and I think we should even follow how these things evolve.