Heat and fluid flow in low Prandtl number melting pools during laser processing of materials are sensitive to the prescribed boundary conditions, and the responses are highly nonlinear. Previous studies have shown that fluid flow in melt pools with surfactants can be unstable at high Marangoni numbers. In numerical simulations of molten metal flow in melt pools, surface deformations and its influence on the energy absorbed by the material are often neglected. However, this simplifying assumption may reduce the level of accuracy of numerical predictions with surface deformations. In the present study, we carry out three-dimensional numerical simulations to realise the effects of surface deformations on thermocapillary flow instabilities in laser melting of a metallic alloy with surfactants. Our computational model is based on the finite-volume method and utilises the volume-of-fluid (VOF) method for gas-metal interface tracking. Additionally, we employ a dynamically adjusted heat source model and discuss its influence on numerical predictions of the melt pool behaviour. Our results demonstrate that including free surface deformations in numerical simulations enhances the predicted flow instabilities and, thus, the predicted solid-liquid interface morphologies.