The South African desert region divided into the Great Karoo and Little Karoo is the Karoo.
More precisely, the Karoo is a broad semi-desert natural region rather than a single uniformly defined desert. Its boundaries are partly geographic, geological, and climatic, and different sources draw them somewhat differently. The Great Karoo is the larger northern section, while the Little Karoo, also called the Klein Karoo, is a narrower valley farther south.
The Swartberg Mountains separate the two regions. The Great Karoo lies north of the range and is divided internally by the Great Escarpment into Upper and Lower Karoo. The Little Karoo occupies a long valley between the Swartberg to the north and the Langeberg–Outeniqua ranges to the south.
This area is famous for sparse, drought-resistant vegetation, dramatic temperature extremes, fossil-rich rocks, and sheep and ostrich farming. The term “desert” can cause confusion because reference works often call the Karoo a semidesert. That classification does not make the stored answer wrong: Karoo is the umbrella geographic name asked for.