With cloud storage, users can store their data files on a remote cloud server with a high quality on-demand cloud service and are able to share their data with other users. Since cloud servers usually are not regarded as fully trusted and the cloud data can be shared amongst users, the integrity checking of the remote files has become an important issue. A number of remote data integrity checking protocols have been proposed in the literature to allow public auditing of cloud data by a third party auditor (TPA). However, user privacy is not taken into account in most of the existing protocols. We believe that preserving the anonymity (i.e., identity privacy) of the data owner is also very important in many applications. In this paper,we propose a new remote integrity checking scheme which allows the cloud server to protect the identity information of the data owner against the TPA. We also define a formal security model to capture the requirement of user anonymity, and prove the anonymity of the proposed scheme. Moreover, we improve the existing security model for data privacy against the TPA, and show that an extended version of our protocol is secure under the strengthened security model.