  We report an x-ray emission spectroscopy (XES) study of the local fluctuating
magnetic moment ($\mu_{bare}$) in $\mathrm{NaFe_{1-x}Co_{x}As}$ and
$\mathrm{NaFe_{1-x}Cu_{x}As}$. In NaFeAs, the reduced height of the As ions
induces a local magnetic moment higher than $\mathrm{Ba_2As_2}$, despite lower
T$_N$ and ordered magnetic moment. As NaFeAs is doped with Co $\mu_{bare}$ 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 of
$\mu_{bare}$ with temperature in all samples as observed in electron- and
hole-doped $\mathrm{BaFe_2As_2}$. 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.
