Decentralized, tamper-proof blockchain is regarded as a solution to a challenging authentication issue in the Internet of Vehicles (IoVs). However, the consensus time and communication overhead of blockchain increase significantly as the number of vehicles connected to the blockchain. To address this issue, vehicular fog computing has been introduced to improve efficiency. However, existing studies ignore several key factors such as the number of vehicles in the fog computing system, which can impact the consensus communication overhead. Meanwhile, there is no comprehensive study on the stability of vehicular fog composition. The vehicle movement will lead to dynamic changes in fog. If the composition of vehicular fog is unstable, the blockchain formed by this fog computing system will be unstable, which can affect the consensus efficiency. With the above considerations, we propose an efficient and stable identity authentication (ESIA) empowered by hierarchical blockchain and fog computing. By grouping vehicles efficiently, ESIA has low communication complexity and achieves high stability. Moreover, to enhance the consensus security of the hierarchical blockchain, the consensus process is from the bottom layer to the up layer (bottom-up), which we call B2UHChain. Through theoretical analysis and simulation verification, our scheme achieves the design goals of high efficiency and stability while significantly improving the IoV scalability to the power of 1.5 (^1.5) under similar security to a single-layer blockchain. In addition, ESIA has less communication and computation overhead, lower latency, and higher throughput than other baseline authentication schemes.