Sixth-generation (6G) space-air-ground integrated vehicular networks (SAGIVNs) are expected to provide customized edge computing services for moving vehicles (MVs). In this article, by integrating 6G SAGIVNs and edge computing, we propose a secure and personalized vehicular edge computing framework in 6G to satisfy the diversified requirements of MVs. In the framework, we first develop a collaborative edge computing mechanism, where each 6G infrastructure (e.g., satellite, drone, and base station) cooperates with parked vehicles to provide services for MVs in order to improve the efficiency of the edge computing services. Then, considering the security issues, a smart-contract-based secure collaboration mechanism is designed to establish a reliable transaction environment for edge computing in 6G. Next, based on the personalized service requirements of MVs and the available resources in 6G SAGIVNs, the resource allocation strategy of each infrastructure and the competitiveness of different infrastructures are discussed to provide MVs with the optimal personalized service. After that, compared with the conventional schemes, a case is studied to evaluate the effectiveness of the proposed framework. Finally, we outline open research topics to identify future research opportunities and directions.