More and more people are concerned about data privacy and this is applicable to vehicular scenarios in which on-board units (OBU) and user devices are exposed to traceability across different access networks and service domains. General Data Protection Regulation (GDPR) in European countries indicates the way to proceed to guarantee privacy and access to sensitive data, however, applying these laws is not straightforward and may vary from country to country. Last advances in 5G communications, such as virtualisation and Multi-Access Edge Computing (MEC) can enable the proper management of data considering local GDPR regulations by using edge services. In this paper we propose the treatment of personal data in virtual OBUs (vOBU) instantiated at the edge of the network on the move. This way, vehicles and occupants benefit from GDPR guarantees compliant with current country regulations as they move across European borders.