The goal of the article is to describe proper names using assumptions of Game Theory. The paper presents a definition of the onymic game and three criteria of distinguishing these games. The first criterion takes into account the goal to be reached by a would-be (potential) onymic game, the second takes into consideration the way a name is formed, whereas the last one characterizes the kind of material used to create the name, i.e. the type of the text (intertext, metatext, context). The theory of games used in this article allows providing a multi-tiered description of onyms. This complex description clearly indicates that 'nomina propria' are heterogeneous. The simultaneous application of the three proposed criteria enables us to distinguish many types of names and to create a typology of distinct and exclusive designations of nouns which includes all types of proper names regardless of their putative designatum.