We report an x-ray emission spectroscopy study of the local fluctuating magnetic moment (μbare) in NaFe1−xCoxAs and NaFe1−xCuxAs. In NaFeAs, the reduced height of the As ions induces a local magnetic moment higher than BaFe2As2 despite lower TN and ordered magnetic moment. As NaFeAs is doped with Co, μbare is slightly reduced, whereas Cu doping leaves it unaffected, indicating a different doping mechanism: based on electron counting for Co, whereas impurity scattering dominates in the case of Cu. Finally, we observe an increase in μbare with temperature in all samples as observed in electron- and hole-doped BaFe2As2. Since both Co and Cu doping display superconductivity, our findings demonstrate that the formation of Cooper pairs is not connected with the complete loss of fluctuating paramagnetic moments.