IPv4 private addresses are commonly used in local area networks (LANs). With the increasing popularity of virtual private networks (VPNs), it has become common that a user connects to multiple LANs at the same time. However, private address ranges for LANs frequently overlap. In such cases, existing systems do not allow the user to access the resources on all LANs at the same time. In this paper, we propose name-based address mapping for VPNs, a novel method that allows connecting to hosts through multiple VPNs at the same time, even when the address ranges of the VPNs overlap. In name-based address mapping, rather than using the IP addresses used on the LANs (the real addresses), we assign a unique virtual address to each remote host based on its domain name. The local host uses the virtual addresses to communicate with remote hosts. We have implemented name-based address mapping for layer 3 OpenVPN connections on Linux and measured its performance. The communication overhead of our system is less than 1.5% for throughput and less than 0.2ms for each name resolution.