A feature is generated by referring to topological entities in a solid model. It is essential to persistently name the topological entities referenced by the feature. This problem is known as the persistent naming problem. The persistent naming problem is divided into naming and name matching. The persistent naming problem is an important issue in the exchange of feature-based CAD models through a neutral format. If a CAD model contains only construction history, the naming of the topological entities is required during translation. However, if a CAD model contains modification history as well, name matching is also required. In a previous study, the authors proposed a naming method for exchanging feature-based CAD models. In this study, a solution to the name matching problem is proposed and its technical details are discussed. The proposed name matching method is based on the local matching technique, using topology merging and splitting history. The feasibility of the proposed name matching method has been demonstrated through experiments with a prototype CAD model translator.