The current Internet architecture was not designed to easily accommodate mobility because IP addresses are used both to identify and locate hosts. The Locator/Identifier Separation Protocol (LISP) decouples them by considering two types of addresses: Endpoint IDentifiers (EIDs) to identify hosts, and Routing LOCators (RLOCs) that identify network attachment points. LISP, with such separation in place, also offers native mobility. In this context, LISP-MN is a particular case of LISP and specifies mobility. Mobility protocols have an inherent issue with privacy since some users may not want to reveal their location or their identity. In this paper, we present an overview of LISP-MN and propose solutions to enable privacy, both in terms of location and identity.