Droste rhymes with:
engrossed, grossed, roast, boast, coast, coste, diagnosed, engrossed, ghost, grossed, host, ivory-coast, khost, most, ost, post, riposte, roast, toast, toste, voest, woeste, yoast, yost
Droste sounds like:
darkest, darst, dearest, deregt, derossett, detract, detracted, dewhirst, dewhurst, direct, directed, direst, dorset, dorsett, dorst, drackett, dragged, draught, dressed, driest, drost, drought, drozd, drozda, drugged, druggist, duerst, durst