We investigate the effect of H adsorption on the magnetic properties of individual Co atoms on Pt(111) with scanning tunneling microscopy. For pristine Co atoms, we detect no inelastic features in the tunnel spectra. Conversely, CoH and CoH2 show a number of low-energy vibrational features in their differential conductance identified by isotope substitution. Only the fcc-adsorbed species present conductance steps of magnetic origin, with a field splitting identifying their effective spin as S-eff = 2 for CoH and 3/2 for CoH2. The exposure to H-2 and desorption through tunnel electrons allow the reversible control of the spin in half-integer steps. Because of the presence of the surface, the hydrogen-induced spin increase is opposite to the spin sequence of CoHn molecules in the gas phase.