Phase change heat transfer allows high heat transfer rates associated with small temperature variations. Given that this technique is employed in several energy and industry applications, such as automotive air-conditioning evaporators, pulsating heat pipes are used for aerospace thermal management and in semiconductor-manufacturing heat exchangers. Although phase change heat transfer has served mankind for more than two millennia, little progress has been made in the last 40 years regarding the basic performance of phase change heat transfer surfaces. However, laser texturing is expected to change this scenario through wettability modification of heat exchanger surfaces, which can lead to heat transfer improvement. In this context, surface texturing of electrolytic copper (a material commonly employed in phase change heat transfer applications) was performed using a nanosecond pulsed fiber laser source associated to a galvanometric scanner. A design of experiments was performed in order to correlate the parameters’ pulse overlapping, laser power, number of scanning repetitions, and pulse duration to their respective machining features. Machining depth and width were evaluated, as well as the surface integrity of the processed region. These analyses were performed by means of white light interferometry, optical microscopy, and scanning electron microscopy. The surface integrity analysis is especially important, since there is a lack of information regarding texturing effects on surface properties, as most studies focus almost exclusively on surface topography and not on the thermal effects that laser texturing can promote to the substrate material. After comprehending the parameter effects on the machining features, surface textures were manufactured and evaluated in order to define their effect over surface wettability, which influences the heat transfer performance. Copper oxide present on the laser generated textures granted them hydrophilicity so that most of the tested textures achieved contact angles of 0°. A cleaning process with H2SO4 was proposed to remove this oxide and decrease the wettability, also allowing hydrophobic surfaces with a contact angle up to 180° to be obtained.