Because of the heterogeneity of resources, diversity of ownership, and decentralization of application management, the traditional pyramid-styled name service is no longer suitable for the Internet of Things (IoT). In order to avoid monopolistic control on IoT name service which is caused by a single root node, some researches have been done to create a federated name service. Yet a simple union of all existing name services cannot guarantee the equality of all participants. Based on the Identity Based Encryption (IBE) technology, we design an equitable federated name service for the IoT. First, Node Mapping Table (NMT) is distributed to each root nodes, which can effectively overcome the shortcomings of the centralized management. Second, the notification of creating or updating NMT will be digitally signed by multiple authorities together to ensure the real equity and fairness of the NMT.