Using angle-resolved photoemission spectroscopy, we studied the evolution of electronic structure of NaFe sub(1-x)Co sub(x)As from an optimally doped superconducting compound (x = 0.028) to a heavily overdoped nonsuperconducting one (x = 0.109). As in "122"-type iron pnictides, our data suggest that the Co dopant in NaFe sub(1-x)Co sub(x)As supplies extra charge carriers and shifts the Fermi level accordingly. The overall band renormalization remains basically the same throughout the doping range we studied, suggesting that the local magnetic and electronic correlations are not affected by carrier doping. In the x = 0.109 compound, the holelike bands around the zone center Gamma move to deeper binding energies and an electron pocket appears instead, resulting in a Fermi surface topology similar to that of A sub(x)Fe sub(2-y)Se sub(2) (A = K, Cs, Rb, Tl). Our data suggest that a balance between itinerant properties of mobile carriers and local interactions plays an important role for the superconductivity in these materials.