In this pioneering study for identifying atomic scale magnetic moment, a single hydrogen atom chemisorbed on pristine graphene exhibits distinct spin polarization. Using first-principles calculations and analyses, we demonstrate that the binding between a H adsorbate and a C substrate is substantially enhanced via compensated B-N pairs embedded into graphene. Surprisingly, the interaction can be further enhanced via non-compensated B-N pair doping. Our established prototype of orbital intercoupling between H 1s and hybridized pz of gapped band edges gives an insight into the enhancing mechanism. For compensated B-N doping, the conduction band minimum (CBM) is pushed upward, which induces stronger interaction between the H 1s and hybridized pz orbitals of the CBM. For non-compensated B-N doping, the orbital interaction occurs between H 1s and hybridized pz orbitals of valence band maximum, thus further lowering the resulting bonding energy due to the enlarged gap. This significantly enhanced interaction between H and C atoms agrees well with the results of charge localization at the gapped band edges. More importantly, the corresponding magnetic moments can be well maintained or even enhanced in both doping; here, one more H atom is needed for non-compensated doping, where its electron occupies the empty CBM. Our findings might provide an effective and practical way to enhance the energetic and magnetic stability of atomic scale magnetic moment on graphene and extensively expand the conception of non-compensated doping.