Vehicular edge computing (VEC) is introduced to extend computing capacity to vehicular network edge recently. With the advent of VEC, service providers directly host services in close proximity of mobile vehicles for great improvements. As a result, a new networking paradigm, vehicular edge networks is emerged along with the development of VEC. However, it is necessary to address security issues for facilitating VEC well. In this paper, we focus on reputation management to ensure security protection and improve network efficiency in the implementation of VEC. A distributed reputation management system (DREAMS) is proposed, wherein VEC servers are adopted to execute local reputation management tasks for vehicles. This system has remarkable features for improving overall performance 1) distributed reputation maintenance; 2) trusted reputation manifestation; 3) accurate reputation update; and 4) available reputation usage. In particular, we utilize multi-weighted subjective logic for accurate reputation update in DREAMS. To enrich reputation usage in DREAMS, service providers optimize resource allocation in computation offloading by considering reputation of vehicles. Numerical results indicate that DREAMS has great advantages in optimizing misbehavior detection and improving the recognition rate of misbehaving vehicles. Meanwhile, we demonstrate the effectiveness of our reputation-based resource allocation algorithm.