The story
* As an English surname, variant of Reeve with excrescent -s. * Also as an English topographical surname, from a misdivision of the Middle English phrase atter eves (“at the border”), see Eaves. * As an Irish surname, from Ó Rímheadha, Ó Rímheá (“descendant of Rímheadh”), from rímid (“counter”).
Etymology from Wiktionary, CC BY-SA 4.0.