Of Old Norse origin, from ei ‘ever, always’ (or einn ‘one, alone’) + ríkr ‘ruler’ (see Eirik). It was introduced into Britain by Scandinavian settlers before the Norman Conquest. As a modern given name, it was revived in the mid 19th century and has remained in use since.
Origin unidentified; possibly 1. French: metronymic from Rousse, a feminine form of Roux meaning ‘redhaired’. 2. Frenchified spelling of Dutch De Roos or of Derous, a habitational name for someone from any of the places in Belgium called Roux, in Hainault, Liège, and Namur provinces.