Abstract: Based on the model representation used in 3D parametric CAD systems,four fundamental conditions to solve the persistent topological naming problem,and their internal relationships are analyzed. The persistent naming problem can be classified into two categories：how to uniquely name and retrieve topological entities,and how to retrieve topological entities as the topological structure of the B-rep model is changed during the re-evaluation process. The first category includes two aspects：how to associate the original name with the B-rep model,and how to construct the reference name.The second category involves two processing methods according to the reference purpose：referring to the geometrical information of the entity,and referring to the entity itself. The naming problems in related domains are also summarized. Opens Issues for further research are discussed.