The genus Roepera is named after the German botanist Johannes Christian Roeper (1801-1885). The former genus name Zygophyllum is derived from the Greek words, zygos, meaning ‘joined’, and phyllon, meaning ‘leaf’, in reference to the paired leaves in so many of the species. Linnaeus was first to established this name in 1753 based on the species Zygophyllum fabago. The species name flexuosum is Latin for ‘pliant’ and is likely in reference to its bendable angular stems.

The genus Roepera belongs to the family Zygophyllaceae, a small, cosmopolitan family of about 26 genera and 280 species, known from arid to tropical and warm regions of the world. In 1814 Robert Brown recognised the family Zygophyllaceae as a distinct taxon under the name Zygophylleae. There are approximately 120 species in the family, of which ± 60 species are found in sub-Saharan Africa, with ± 45-50 species in southern Africa. There are also species found in the Mediterranean countries, Asia, Australia, Chile and the United States. In the southern Africa region, the species are prevalent in both winter- and summer rainfall-areas, irrespective of rainfall. The two areas with the greatest number of species present in South Africa are the Nama-Karoo and Succulent Karoo Biomes. The Gariep Centre, in the Northern Cape, is considered the principal centre of diversity and endemism for the genus in southern Africa.

Recent DNA studies in the Zygophyllaceae have caused substantial changes in the ordering of genera and species. This species was originally placed in the genus Zygophyllum until the results of a 2003 study caused it to be moved into the genus Roepera, but it was then proposed that it be moved back to Zygophyllum by a 2008 study that refuted the 2003 study. However, after more studies, it is now largely accepted that Zygophyllum is an Asian genus and the southern African species formerly placed in Zygophyllum are divided into two genera: Roepera formerly subgenus Zygophyllum; and Tetraena formerly subgenus Agrophyllum. Species of Roeperia, including R. morgsana, are characterised by petals with markings at the base or streaked with red veins, a papillate disc and fruit disintegrating when mature. For species in the genus Tetraena, including T. simplex, the petals lack markings at the base, the disc is smooth, and the fruit splits into five parts (mericarps).

This species was named vyfpondbos in the 1950s when an agricultural officer gave a lecture in the field at Zebra in the Oudtshoorn-district (Klein-Karoo region of the Western Cape). This came about when someone in the audience wanted to know whether this plant has a common name in discussing the merits of the plant. The officer replied that despite not being in possession of such, in his opinion each plant, undoubtedly given its grazing-value, as at least worth five pounds (vyf pond). Since then it has been referred to as vyfpondbos. The name spekbossie also refers to its qualities as grazing, because the animals that graze on it are said to become spekvet (as fat as pigs).