The Ethereum network suffers at the moment from a serious of privacy problem, every transaction is visible to the whole world. Perhaps, it might be an advantage in the direction of simple transaction validation, but it is a huge drawback in the direction of privacy. Even if public keys are not bound to an identity by default, if the identity is confidently leaked, the whole transaction network of an individual will be visible. It is simply not an acceptable.
On solution might be the introduction of the Bitcoin style HD wallets, that simply creates a new address at each transaction. Certainly, it works well as we need only to transfer Ether or coins, however the situation might be a little be complicated as soon we need general smart contracts and access rights of the contracts . It is an open question how the HD wallet concept can be extended to cover general smart contracts with access rights as well.
A second possibility is to use mixers or similar functionalities. One way might be to use directly mixers as on the top of Ethereum blockchain, the second one is to build mixers indirectly into the protocol. However at both cases the problem is not exactly same as at the Bitcoin blockchain: as we simply transfer ether everything works fine, however as soon we have more complicated use-cases and general smart contracts, the model will be again difficult.
The third option might be to generally change the open style of the platform to a more private one. A simple solution might be to use Ethereum in a consortium Blockchain scenario. A more complicated is perhaps to build zero knowledge proof into the platform and consensus algorithm itself, implying more privacy by default. Certainly, the way of doing this is pretty difficult not only from a practical but a theoretical one as well.