Cadaba aphylla (SA Tree No. 129) is called desert broom, firstly because it lives well in extreme or semi-desert climate conditions of drought, frost or heat and secondly because the absence of leaves brings a resemblance to another plant, Cytisus scoparius or common broom, a southern European arid region, leafless plant that has yellow flowers (and is a serious invader in North America, Australia, New Zealand and maybe elsewhere).
The Afrikaans names of swartstorm (black storm) and bobbejaanarm (baboon arm) are interesting, giving leeway to speculation as to their origins, maybe relating to the darkness of the shrub and the shape of old branches. The botanical name is also of interest as it is tautological: both "cadaba" (Greek) and "aphylla" (Greek and Latin origins) mean leafless. It is also sometimes called leafless wormbush.
The plant can be grown from seed and is a good choice for gardens where temperature extremes, no shade and water scarcity provide challenges. More gardeners (and nurseries) should be taking note of the merits of this as a garden plant (www.plantzafrica.com).