We use unpolarized and polarized neutron scattering to study the temperature and polarization dependence of low-energy magnetic fluctuations in nearly optimally doped NaFe0.9785Co0.0215As, with coexisting superconductivity (Tc≈19 K) and weak antiferromagnetic order (TN≈30 K, ordered moment ≈0.02μB/Fe). A single spin resonance mode with intensity tracking the superconducting order parameter is observed, although energy of the mode only softens slightly upon approaching Tc. Polarized neutron scattering reveals that the single resonance is mostly isotropic in spin space, similar to overdoped NaFe0.935Co0.045As but different from optimal electron-, hole-, and isovalently doped BaFe2As2 compounds, all featuring an additional prominent anisotropic component. Spin anisotropy in NaFe0.9785Co0.0215As is instead present at energies below the resonance, which becomes partially gapped below Tc, similar to the situation in optimally doped YBa2Cu3O6.9. Our results indicate that anisotropic spin fluctuations in NaFe1−xCoxAs appear in the form of a resonance in the underdoped regime, become partially gapped below Tc near optimal doping, and disappear in overdoped compounds.