No, Rohirrim is Sindarin for "People of the Horse-Lords". They call themselve Eorlingas (descendants of Eorl the Young). "Riders of Rohan" or "Riders of the Mark" refers specifically to the mounted soldiers.
Half-elven is not Elrond's alias, but rather a descriptor, as he is descended from Beren and Luthien and therefore is only half elven, given the choice to become a man like Elros chose to.