Recent neutron-scattering measurements indicate that NaFe1−xCuxAs forms an antiferromagnetic stripe phase near x≈0.5 in a Mott insulating state. This copper concentration is well in excess of that required for superconductivity, x<0.04. We have investigated the development of magnetism in this compound by using 23Na nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation measurements performed on single crystals (x=0.13, 0.18, 0.24, and 0.39). We find multiple inequivalent Na sites, each of which is associated with a different number of nearest-neighbor Fe sites occupied by a Cu dopant. We show that the distribution of Cu substituted for Fe is random in-plane for low concentrations (x=0.13 and 0.18) but deviates from this with increasing Cu doping. As is characteristic of many pnictide compounds, there is a spin pseudogap that increases in magnitude with dopant concentration. This is correlated with a corresponding increase in orbital NMR frequency shift, indicating a change in valence from Cu2+ to a Cu1+ state as x exceeds 0.18, concomitant with the change of Fe2+ to Fe3+ resulting in the formation of magnetic clusters. However, for x≤0.39 there is no evidence of long-range static magnetic order.