When the classically conformal invariance is imposed on the minimal gauged B−L extended standard model, the B−L gauge symmetry is broken by the Coleman-Weinberg mechanism naturally at the TeV scale. Introducing a new Z₂ parity in the model, we investigate phenomenology of a right-handed neutrino dark matter whose stability is ensured by the parity. We find that the relic abundance of the dark matter particle can be consistent with the observations through annihilation processes enhanced by resonances of either the standard model Higgs boson, the B−L Higgs boson, or the B−L gauge boson (Z′ boson). Therefore, the dark matter mass is close to half of one of these boson masses. Because of the classically conformal invariance and the B−L gauge symmetry breaking via the Coleman-Weinberg mechanism, Higgs boson masses, Z′ boson mass, and the dark matter mass are all related, and we identify the mass region to be consistent with experimental results. We also calculate the spin-independent cross section of the dark matter particle off with nucleon and discuss implications for future direct dark matter search experiments.