Nowadays, many organizations outsource data storage to the cloud such that a member (owner) of an organization can easily share data with other members (users). Due to the existence of security concerns in the cloud, both owners and users are suggested to verify the integrity of cloud data with Provable Data Possession (PDP) before further utilization on data. However, previous methods either unnecessarily reveal the identity of a data owner to the untrusted cloud or any public verifiers, or introduce significant overheads on verification metadata to preserve anonymity. In this paper, we propose a simple and efficient publicly verifiable approach to ensure cloud data integrity without sacrificing the anonymity of data owners nor requiring significant verification metadata. Specifically, we introduce a security-mediator (SEM), which is able to generate verification metadata (i.e., signatures) on outsourced data for data owners. Our approach decouples the anonymity protection mechanism from the PDP. Thus, an organization can employ its own anonymous authentication mechanism, and the cloud is oblivious to that since it only deals with typical PDP-metadata, Consequently, there is no extra storage overhead when compared with existing non-anonymous PDP solutions. The distinctive features of our scheme also include data privacy, such that the SEM does not learn anything about the data to be uploaded to the cloud at all, which is able to minimize the requirement of trust on the SEM. In addition, we can also extend our scheme to work with the multi-SEM model, which can avoid the potential single point of failure existing in the single-SEM scenario. Security analyses prove our scheme is secure, and experiment results demonstrate our scheme is efficient.