Onomastic periphrases, which are cognitively motivated variants of official onyms (toponyms and anthroponyms), form important cultural codes of an ethnic community and shape the linguistic parameters of its national identity. The goal of this article is to interpret the cognitive mechanisms of the formation of periphrases of Latin American toponyms and to present their cognitive schemes. The hypothesis is that toponymic periphrases play the role of knowledge transfer. The author examines the periphrases of Latin American geographical names, primarily the names of Latin American capitals, and proposes their typology. It has been established that the main cognitive schemes of the periphrases include reification and personification. National attribution of periphrases is between uniqueness and polyreferentiality. Moreover, the more abstract is the periphrase, the greater is the probability of its polyreferentiality. Toponymic periphrases are included in the toponymic concepts of the corresponding geographical objects. The obtained results clarify the mechanisms of linguistic creativity and discursive identity of speakers of various Latin American varieties of the Spanish language, and demonstrate the trends in the linguistic parameters of national identity and linguistic creativity in the field of place names.