  The generation of neutrino masses by inverse seesaw mechanisms has advantages
over other seesaw models since the potential new physics can be produced at the
TeV scale. We propose a model that generates the inverse seesaw mechanism via
spontaneous breaking of the lepton number, by extending the Standard Model with
two scalar singlets and two fermion singlets both charged under lepton number.
The model gives rise to a massless Majoron and a massive pseudoscalar which we
dub as massive Majoron, which corresponds to the Nambu-Goldstone boson of the
breaking of lepton number. If the massive Majoron is stable in cosmological
time, it might play the role of a suitable Dark Matter candidate. In this
scenario, we examine the model with a massive Majoron in the keV range. In this
regime, its decay mode to neutrinos is sensitive to the ratio between the vevs
of the new scalars ($\omega$), and it vanishes when $ \omega \simeq
\sqrt{2/3}$, which is valid within a large region in the parameter space. On
the other hand, the cosmological lifetime for the Dark Matter candidate places
constraints on its mass via scalar decays. In addition, simple mechanisms that
explain the Dark Matter relic abundance within this context and plausible
modifications to the proposed setup are briefly discussed.
