Pulsed Laser Surface Melting (pLSM) is a technique that offers an efficient way to modify the geometry surfaces without any addition or removal of material. In pLSM, an incident laser beam melts a small region on the surface and induces surface tension and viscosity-driven flows that modify the surface geometry. Initial surface geometry plays an important role in deciding the melt pool flows and shape as it governs the initial surface tension acting on the melt pool. In this paper, we present a systematic numerical study that captures the effects of initial geometries using a two-dimensional axisymmetric model. The results show that geometries with higher curvatures result in deeper melt pools and higher surface displacement because higher fluid velocities aid the convection heat transfer. Additionally, we define a modified capillary number (CaM) which elegantly captures these effects.