The genus name is the vocalisation of the acronym AMNH of the American Museum of Natural History and the suffix -ia (Aay-Em-En-Aytche-ia), as gratitude for funding Lieberman's research.

The species epithet paragranulata refers to the fact that the species was first regarded as closely related to Dechenella granulata.

[1] A. paragranulata has been collected from the Devonian of Canada (Emsian and Eifelian, Blue Fjord Formation, Bathurst Island, Nunavut).

[1] Aayemenaytcheia paragranulata was originally described as a species belonging to the genus Dechenella.

Recent cladistic analysis however makes it likely the species is in fact the earliest branch of a clade that further includes Lacunoporaspis, Dechenella, Schizoproetus and Schizoproetoides.