An extensive study on doping of two-dimensional (2D) hexagonal boron phosphide (h-BP) which is a direct band gap semiconductor was performed by using ab initio methods based on spin-polarized density functional theory. The interaction of group III-IV-V elements with h-BP is explored, considering both adsorption and substitution cases, and the resulting structural and electronic properties are examined. The variation of adsorption (substitution) energies and band gap values are systematically analyzed and trends are identified. Upon adsorption, the most of the elements bound on top of P atom forming dumbbell geometry which generates characteristic spin-polarized impurity states. The substitution of B or P by group III-IV-V elements can produce extra electrons/holes which lead to n-type and p-type doping for adequate cases. Additionally, doping can further generate impurity resonant states. Functionalization of h-BP with adatoms can tune the electronic structure and would be useful for nanoelectronic applications in low-dimensions.