  Neutron spin resonance, a collective magnetic excitation coupled to
superconductivity, is one of the most prominent features shared by a broad
family of unconventional superconductors including copper oxides, iron
pnictides, and heavy fermions. In this work, we study the doping evolution of
the resonances in NaFe$_{1-x}$Co$_x$As covering the entire superconducting
dome. For the underdoped compositions, two resonance modes coexist. As doping
increases, the low-energy resonance gradually loses its spectral weight to the
high-energy one but remains at the same energy. By contrast, in the overdoped
regime we only find one single resonance, which acquires a broader width in
both energy and momentum, but retains approximately the same peak position even
when $T_c$ drops by nearly a half compared to optimal doping. These results
suggest that the energy of the resonance in electron overdoped
NaFe$_{1-x}$Co$_x$As is neither simply proportional to $T_c$ nor the
superconducting gap, but is controlled by the multi-orbital character of the
system and doped impurity scattering effect.
