To advance towards carbon-neutrality and improve the limited {performance} of conventional passive wireless communications, in this paper, we investigate the integration of noise modulation with zero-energy reconfigurable intelligent surfaces (RISs). In particular, the RIS reconfigurable elements (REs) are divided into two groups: one for beamforming the desired signals in reflection mode and another for harvesting energy from interference signals in an absorption mode, providing the power required for RIS operation. Since the harvested energy is a random variable, a random number of REs can beamform the signals, while the remainder blindly reflects them. We present a closed-form solution and a search algorithm for REs allocation, jointly optimizing both the energy harvesting (EH) and communication performance. Considering the repetition coding technique and discrete phase shifts, we derive analytical expressions for the energy constrained success rate, bit error rate, optimal threshold, mutual information, {and energy efficiency}. Numerical and simulation results confirm the effectiveness of the algorithm and expressions, demonstrating the superiority of the proposed integration over conventional noise-modulation systems. It is shown that by properly allocating the REs, both the EH and communication performance can be improved in low to moderate interference scenarios, while the latter is restricted in the high-interference regime.