Vehicular cloud computing (VCC) is composed of multiple distributed vehicular clouds (VCs), which are formed on-the-fly by dynamically integrating underutilized vehicular resources including computing power, storage, and so on. Existing proposals for identity-as-a-service (IDaaS) are not suitable for use in VCC due to limited computing resources and storage capacity of onboard vehicle devices. In this paper, we first propose an improved ciphertext-policy attribute-based encryption (CP-ABE) scheme. Utilizing the improved CP-ABE scheme and the permissioned blockchain technology, we propose a lightweight and privacy-preserving IDaaS architecture for VCC named IDaaSoVCC. It realizes lightweight and privacy-preserving access control of vehicles' personally identifiable information (PII) in a large distributed vehicular cloud system. Security analysis demonstrates the security features of IDaaSoVCC, most notably forward secrecy, confidentiality and identity information privacy. Meanwhile, we verify that IDaaSoVCC is feasible and practical in a large distributed VC system through extensive simulations.