In this letter, we enhance the performance of wireless communication systems by utilizing reconfigurable intelligent surface (RIS) and index modulation (IM). In particular, we introduce two schemes: RIS-assisted receive generalized space-shift keying (RIS-RGSSK) and RIS-assisted receive generalized spatial modulation (RIS-RGSM). In the RIS-RGSSK scheme, information bits are conveyed through selection of multiple receive antennas. The RIS-RGSM scheme takes RIS-RGSSK a step further by conveying information bits not only through the selection of multiple receive antennas, but also through embedding information bits in the phase of the received signals using M-ary phase shift keying (PSK) modulation. We also present simple yet efficient greedy detectors (GDs) for non-coherent detection of both schemes. Simulation results demonstrate the advantages of our proposed methods over existing schemes such as the RIS-assisted receive quadrature space-shift keying (RIS-RQSSK).