"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. 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. 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. 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.