Geo-distributed mobile cloud computing (GMCC) integrates location information into mobile cloud computing, that has high potential for a large variety of applications. In a vehicular environment, a GMCC provides a large number of resources to vehicles that are geographically close to them. However, there are few studies that focus on security and privacy pseudonym management in GMCC system for vehicular environment. We design a three-layer on-demand pseudonym system to manage the pseudonyms. Moreover, we propose a secure pseudonym distribution scheme for secure communication among vehicles. As the number of demanded pseudonyms varies with traffic loads in different clouds, we use a newsvendor model to address the optimal on-demand pseudonym distribution problem. Numerical results indicate our proposed schemes not only improve utility of the clouds, but also maximize utilization of pseudonyms.