Stainless steel 316L is an austenitic alloy that is widely used in varying industries due to its outstanding corrosion resistance, high strength, and ductility properties. However, the wear and friction resistance properties are low. Laser surface texturing can improve the wear and friction resistance of the material via the functionalisation of the surface. The laser surface texturing efficiency and the texture quality are defined by the material’s surface properties and laser parameters. The surface roughness is an important material property having an effect on laser surface texturing. This paper reports on a study of the material’s surface roughness influence on the texturing of 316L stainless steel with 1064 nm nanosecond pulsed laser. Single pulse shots were employed to avoid the topographic influence of the previous laser shots. The surface shape and the topography of the textures were assessed using optical microscopy and profilometry. It was observed that the textures produced were dimples of U-type and sombrero-like type geometries depending on surface roughness and pulse energy. The overall quality of the texture shape was better for smoother surfaces. The energy fluence necessary to generate textures is lower on surfaces of lower roughness than surfaces with high roughness. The surface at 24 nm of average roughness is the best surface for creating deep textures. The ablation mechanisms associated with high pulse energy, including plasma shielding, are produced at lower pulse energies for the 100 nm roughness, compared with other roughness samples.