  The extension of the Standard model (SM) with three heavy right handed
neutrinos, a complex scalar and the gauged $U(1)_{\rm B-L}$ symmetry (the
minimal $B-L$ model) is considered the most compelling minimal one: the
presence and the out-of-equilibrium decay of the heavy right handed neutrinos
can account for the small masses of the active neutrinos and the baryon
asymmetry of the universe. A natural accompanying question concerns whether the
minimal $B-L$ model can naturally accommodate an interesting dark matter (DM)
candidate. We study the possibility where the current DM population is
explained by the gauge boson of $U(1)_{\rm B-L}$ symmetry. We discuss how the
minimal set-up originally aimed at the seesaw mechanism and the leptogenesis is
connected to conditions making the gauge boson promoted to a DM candidate.
