Due to the high latency and cost of pseudonym management faced by the current Internet of Vehicles (IoV), as well as the inability of existing pseudonym location privacy protection methods to effectively resist pseudonym association attacks, the location privacy protection of existing schemes requires improvements. This study proposes a Fog computing-based Pseudonym Management Program (FPMP). It transfers the management of vehicle pseudonyms to the fog layer to reduce the burden on certificate issuing authorities and reduce the latency of vehicle pseudonym application requests; In order to maximize the efficiency of using pseudonyms, a profit function for generating pseudonyms is derived. A method for distributing vehicle pseudonyms on demand is designed. Furthermore, an algorithm that controls the dynamic pseudonym swap program (DPSP) is proposed to ensure secure transmissions and the location privacy of vehicles. It determines a pseudonym swapping area based on the communication time and the number of vehicles in a region. Experiments indicate that the proposed DPSP achieves 10.1% and 4% higher anonymity entropy than the pseudonym swapping based on neighboring vehicles (PSNV) and the dynamic mixed zone for location privacy (DMLP) algorithms, respectively, for 100 vehicles.