We revisit the problem of local moment formation in graphene due to chemisorption of individual atomic hydrogen or other analogous sp3 covalent functionalizations. We describe graphene with the single-orbital Hubbard model, so that the H chemisorption is equivalent to a vacancy in the honeycomb lattice. To circumvent artifacts related to periodic unit cells, we use either huge simulation cells of up to 8×105 sites, or an embedding scheme that allows the modeling of a single vacancy in an otherwise pristine infinite honeycomb lattice. We find three results that stress the anomalous nature of the magnetic moment (m) in this system. First, in the noninteracting (U=0) zero-temperature (T=0) case, the m(B) is a continuous smooth curve with divergent susceptibility, different from the stepwise constant function found for single unpaired spins in a gapped system. Second, for U=0 and T>0, the linear susceptibility follows a power law T-α with an exponent of α=0.77 different from the conventional Curie law. For U>0, in the mean-field approximation, the integrated moment is smaller than m=1μB, in contrast with results using periodic unit cells. These three results highlight the fact that the magnetic response of the local moment induced by sp3 functionalizations in graphene is different from that of local moments in gapped systems, for which the magnetic moment is quantized and follows a Curie law, and from Pauli paramagnetism in conductors, for which linear susceptibility can be defined at T=0.