They'll know exactly who they are thanks to the Blockchain. Remember that most people that buy bitcoin do it through a regulated service and inexorably have their identities tied to their addresses. Only the very very clever ones will be able to hide their identity from government. And even if they succeeded, their Bitcoins could be blacklisted and thus no miner would include it in their block. This government regulation does not yet exist but it's only a matter of time until they threaten big mining operations into compliance.