Notary cross-chain transaction technologies have obtained broad affirmation from industry and academia as they can avoid data islands and enhance chain interoperability. However, the increased privacy concern in data sharing makes the participants hesitate to upload sensitive information without the trust foundation of the external network. To address this issue, this paper proposes a differential private notary mechanism (DPNM) to preserve privacy in blockchain interoperations. It establishes a fully trusted notary organization to conduct data perturbation before replying query to the external blockchain network. In addition, the DPNM contains two built-in privacy budget allocation schemes: Efficiency priority scheme (EPS) and Privacy priority scheme (PPS). These schemes unify the privacy preferences among different nodes based on multi-node consensus in the decentralized environment. The EPS can generate noise linearly and work efficiently, and the PPS reflects better on nodes' preferences. This paper utilizes several metrics including mechanism errors, elapsed time, latency, and gas consumption to evaluate the performance of DPNM compared to the traditional mechanisms. The experiment results indicate that the proposed mechanism can meet privacy preferences among different nodes and provide better utility with little extra cost.