This paper aims at describing several phenomena related to the reference of proper nouns in terms of the mental space theory. Mental spaces are very partial assemblies constructed as we think and talk, for purposes of local understanding and action. They contain elements and are structured by frames and cognitive models. Mental spaces are connected to long-term schematic knowledge, and to long-term specific knowledge. Mental spaces are constructed and modified as thought and discourse unfolds and are connected to each other by various kinds of mappings, in particular identity and analogy mappings. Spaces are built up from many sources. There are various kinds of space-builders to construct various spaces. Elements which belong to the spaces which are introduced by space-builders can be identified by the identification principle. There are several sentences including proper nouns which have been described by the description theory or the reference theory for proper names and have been problematic to the two theories. However these sentences are successfully described in terms of the mental space theory.