Holographic near-eye displays offer ultra-compact form factors for VR/AR systems but rely on advanced computer-generated holography (CGH) algorithms to convert 3D scenes into interference patterns on spatial light modulators (SLMs). Conventional CGH typically generates smooth-phase holograms, limiting view-dependent effects and realistic defocus blur, while severely under-utilizing the SLM space-bandwidth product. We propose Random-phase Wave Splatting (RPWS), a unified wave optics rendering framework that converts arbitrary 3D representations based on 2D translucent primitives into random-phase holograms. RPWS is fully compatible with modern 3D representations such as Gaussians and triangles, improves bandwidth utilization which effectively enlarges eyebox size, reconstructs accurate defocus blur and parallax, and leverages time-multiplexed rendering not as a heuristic for speckle suppression, but as a mathematically exact alpha-blending mechanism derived from first principles in statistics. At the core of RPWS are (1) a new wavefront compositing procedure and (2) an alpha-blending scheme for random-phase geometric primitives, ensuring correct color reconstruction and robust occlusion when compositing millions of primitives. RPWS departs substantially from the recent primitive-based CGH algorithm, Gaussian Wave Splatting (GWS). Because GWS uses smooth-phase primitives, it struggles to capture view-dependent effects and realistic defocus blur and under-utilizes the SLM space-bandwidth product; moreover, naively extending GWS to random-phase primitives fails to reconstruct accurate colors. In contrast, RPWS is designed from the ground up for arbitrary random-phase translucent primitives, and through simulations and experimental validations we demonstrate state-of-the-art image quality and perceptually faithful 3D holograms for next-generation near-eye displays.