The rapid development of connected and intelligent transportation systems has increased the adoption of Vehicular Ad Hoc Networks (VANETs) for vehicle sharing and rental services. However, vehicle renting in VANETs introduces significant security and privacy challenges, including unauthorized access, identity disclosure, driver tracking, Sybil attacks, credential misuse, and difficulties in establishing accountability. Conventional authentication approaches often rely on persistent identities, which can compromise driver privacy, while fully anonymous mechanisms may make it difficult to identify malicious users when security incidents occur. This paper presents a privacy-preserving and zero-trust approach for secure vehicle renting in VANETs that integrates anonymous authentication, controlled accountability, and Sybil resistance. The proposed framework follows a zero-trust principle in which vehicles, drivers, and service entities are not implicitly trusted and access requests are subjected to appropriate verification before rental resources are authorized. Privacy-preserving credentials are used to minimize unnecessary disclosure of driver identities, while conditional traceability enables an authorized entity to establish the identity of a malicious participant when required. The framework also incorporates mechanisms to restrict the creation and misuse of multiple pseudonymous identities, thereby strengthening resistance against Sybil attacks. A security analysis is presented against major threats, including impersonation, replay, man-in-the-middle, credential misuse, and Sybil attacks. The paper further discusses computational and communication considerations, scalability, and practical deployment challenges. The proposed approach provides a unified perspective for achieving secure, privacy-aware, and accountable vehicle-rental services in future connected vehicular environments.