Banksia prionotes was first published by English botanist John Lindley in the January 1840 issue of his A Sketch of the Vegetation of the Swan River Colony; hence the species' standard author citation is Banksia prionotes Lindl.[1] He did not specify the type material upon which he based the species, but A Sketch of the Vegetation of the Swan River Colony is based primarily upon the collections of early settler and botanist James Drummond.[8] A sheet of mounted specimens at the University of Cambridge Herbarium (CGE), labelled "Swan River, Drummond, 1839" and annotated "Banksia prionotes m" in Lindley's hand, has since been designated the lectotype.[3] Lindley also made no mention of the etymology of the specific epithet, "prionotes", but it is assumed to be derived from the Ancient Greek prion ("saw") and -otes ("quality"), referring to the serrated leaf margins.[9]