In Named Data Networking (NDN), data synchronization plays an important role similar to transport protocols in IP. Many distributed applications, including pub-sub applications such as news and weather services, require a synchronization protocol where each consumer can subscribe to a different subset of a producer's data streams. However, existing Sync protocols support only full-data synchronization, which is a special case of this problem. We propose PSync to efficiently address different types of data synchronization. Names are used in PSync messages to carry producers' latest namespace information and each consumer's subscription information, which allows producers to maintain a single state for all consumers and enables consumers to synchronize with any producer that replicates the same data. We have implemented PSync in the NDN codebase and used it to develop a prototype pub-sub module for building management. Our experimental results show that PSync scales well as the number of consumers, subscriptions, and data streams increases and it outperforms the state-of-the-art Sync protocol in supporting full-data synchronization.