Zeuglodon paulsonii was named by Brandt (1873) [The type specimen is in the Anatomical Museum of the University of Kiev according to Kellogg (1936): no number is available. See Brandt 1873b, plate 34. The holotype of Platyosphys paulsonii is not available for study at present. In 1920s it was probably relocated from the Anatomical Museum of Kiev University (now National Museum of Medicine of Ukraine) to the university itself, and it was never recorded or seen after the World War II. Thus, this type specimen is considered to be lost, and the name Platyosphys paulsonii is considered as nomen dubium (Gol'din & Zvonok 2013). ]. Its type specimen is no number listed, a set of vertebrae, and it is a 3D body fossil. Its type locality is Chigirin, which is in a Priabonian marine claystone in Ukraine.

It was recombined as Basilosaurus paulsoni by Trouessart (1904) and Dubrovo and Kapelist (1973); it was recombined as Platyosphys paulsonii by Kellogg (1936), Gingerich and Zouhri (2015) and van Vliet et al. (2019); it was recombined as Platyosphys paulsoni by Mchedlidze (1970) and van Vliet (2004); it was considered a nomen dubium by Uhen (2013) and Goldin and Zvonok (2013); it was recombined as Pachycetus paulsonii by van Vliet et al. (2020) and Gingerich et al. (2022).