  We revisit the dynamical generation of an arbitrarily small neutrino Yukawa
coupling in the Standard Model with trans-Planckian asymptotic safety and apply
the same mechanism to the gauged $B-L$ model. We show that thanks to the
presence of additional irrelevant couplings, the described neutrino-mass
generation in the $B-L$ model is potentially more in line with existing
theoretical calculations in quantum gravity. Interestingly, the model can
accommodate, in full naturalness and without extensions, the possibility of
purely Dirac, pseudo-Dirac, and Majorana neutrinos with any see-saw scale. We
investigate eventual distinctive signatures of these cases in the detection of
gravitational waves from first-order phase transitions. We find that, while it
is easy to produce a signal observable in new-generation interferometers, its
discriminating features are washed out by the strong dependence of the
gravitational-wave spectrum on the relevant parameters of the scalar potential.
