Information-centric networking (ICN) is an emerging network architecture that has the potential to address demands related to transmission latency and reliability in fifth-generation (5G) communication technology and the Internet of Things (IoT). As an essential component of ICN, name resolution provides the capability to translate identifiers into locators. Applications have different demands on name-resolution latency. To meet the demands, deploying name-resolution servers at the edge of the network by dividing it into multilayer overlay networks is effective. Moreover, optimization of the deployment of distributed name-resolution servers in such networks to minimize deployment costs is significant. In this paper, we first study the placement problem of the name-resolution server in ICN. Then, two algorithms called IIT-DOWN and IIT-UP are developed based on the heuristic ideas of inter-layer information transfer (IIT) and server reuse. They transfer server placement information and latency information between adjacent layers from different directions. Finally, experiments are conducted on both simulation networks and a real-world dataset. The experimental results reveal that the proposed algorithms outperform state-of-the-art algorithms such as the latency-aware hierarchical elastic area partitioning (LHP) algorithm in finding more cost-efficient solutions with a shorter execution time.