  We consider minimal $U(1)$ extensions of the Standard Model in which one of
the right-handed neutrinos is charged under the new gauge symmetry and plays
the role of dark matter. In particular, we perform a detailed phenomenological
study for the case of a $U(1)_{(B-L)_3}$ flavoured $B-L$ symmetry. If
perturbativity is required up to high-scales, we find an upper bound on the
dark matter mass of $m_\chi\lesssim2$ TeV, significantly stronger than that
obtained in simplified models. Furthermore, if the $U(1)_{(B-L)_3}$ breaking
scalar has significant mixing with the SM Higgs, there are already strong
constraints from direct detection. On the other hand, there remains significant
viable parameter space in the case of small mixing, which may be probed in the
future via LHC $Z^\prime$ searches and indirect detection. We also comment on
more general anomaly-free symmetries consistent with a TeV-scale RH neutrino
dark matter candidate, and show that if two heavy RH neutrinos for leptogenesis
are also required, one is naturally led to a single-parameter class of $U(1)$
symmetries.
