The article explores the use of proper names as a source of wordplay in the classroom bilingual interaction in English as a second language. It is noted that wordplay becomes a means of accommodation to the onomastic system of a foreign language when proper names trigger bilingual metalinguistic reflection. The author emphasizes that wordplay is a process of deliberate deviation from language norms in which the proper name is a standard language unit (‘normema’) that undergoes linguistic reinterpretation and turns into a non-standard language unit (‘igrema’) developing both formal and semantic changes. It is exactly the non-standard nature of onomastic units under study and the specificity of the material that explain the novelty of the present research. This paper aims to identify the reasons why proper names become a source of non-standard language units in the classroom bilingual speech. Two groups of such reasons are distinguished, namely, the features of the formal morphological structure of proper names and features of their lexical meaning. It appears that wordplay occurs in proper names that include a ‘transferable’ component, creating an associative metatextual reference in the bilingual mind. Proceeding from the fact that such components can be found on the phonemic, morphemic, or lexical level, the author describes three corresponding models of wordplay. It is noted that wordplay mostly involves proper names with a distinct social component that is also relevant in the community of native English speakers. These include personal and place names, names of organizations and products. For each type of proper names, the author suggests two types of the development of the semantic connection between a standard language unit and a non-standard language unit: the one that does not involve the internal form of a proper name and another one that is based on it.