A ro-vibrationally inelastic close coupling study of the rotational excitation of OH+(X-3 Sigma(+)) by collisions with H(S-2) is presented. The two lowest potential energy surfaces of doublet and quadruplet spin multiplicity are involved. The former is the one we developed recently, and the latter is a modified version of the quadruplet surface of Martinez et al. to include the long-range charge-induced-dipole potential. The details of the modification of this surface are presented as well as the comparison of the rotational excitation resulting from collisions with hydrogen on these two surfaces. The effect of the coupling between vibration and rotation on the rotational excitation rate is also discussed, as the potential well depth of the doublet surface is quite large and allows the coupling between many vibrational channels of OH+. As the hydrogen exchange reaction can occur for both potential energy surfaces, we discuss the reliability of the approximation made by the calculation of the cross sections with a quantum dynamics limited to the inelastic process. The relative importance of the collisions on the doublet or quadruplet surface within a given rotational transition is also discussed.