In a beyond-5G (B5G) scenario, we consider a virtual private mobile network (VPMN), i.e., a set of user equipments (UEs) directly communicating in a device-to-device (D2D) fashion, and connected to the cellular network by multiple gateways. The purpose of the VPMN is to hide the position of the VPMN UEs to the mobile network operator (MNO). We investigate the design and performance of packet routing inside the VPMN. First, we note that the routing that maximizes the rate between the VPMN and the cellular network leads to an unbalanced use of the gateways by each UE. In turn, this reveals information on the location of the VPMN UEs. Therefore, we derive a routing algorithm that maximizes the VPMN rate, while imposing for each UE the same data rate at each gateway, thus hiding the location of the UE. We compare the performance of the resulting solution, assessing the location privacy achieved by the VPMN, and considering both the case of single hop and multihop in the transmissions from the UEs to the gateways.