Originally just the shrub whose branches made sweeping tools — the tool took the plant's name by metonymy.
A long-handled brush used for sweeping floors; also, a thorny shrub of the pea family with yellow flowers.
From Old English 'brōm,' originally meaning the shrub (Cytisus scoparius), not the cleaning tool. The shrub's long, straight, flexible branches were bundled and tied to handles to make sweeping implements, and the tool gradually took on the plant's name. The Proto-Germanic form was *brāmō, meaning 'thorny shrub.' The same root