Trigonotreta stokesii was named by Koenig (1825). Its type specimen is BMNH B4798 and is a 3D body fossil. Its type locality is Insula Van Diemen Novae Hollandiae, which is in a Sakmarian coastal sandstone in the Swifts Jetty Sandstone Formation of Australia.

It was recombined as Spirifer stokesii by Morris (1845); it was recombined as Spiriferina stokesi by Reed (1932); it was corrected as Trigonotreta stokesi by Clarke (1979), Clarke (1990), Clarke (1992), Cisterna and Shi (2014).