  We employ {\it{ab-initio}} calculations to investigate the charge density
waves in single-layer NbSe$_2$, and we explore how they are affected by
transition metal atoms. Our calculations reproduce the observed orthorhombic
phase in single-layer NbSe$_2$ in the clean limit, establishing the energy
order between three different distorted structures, two consisting of
triangular Nb-Nb clusters and a third, energetically unfavoured, consisting of
hexagonal Nb-Nb clusters. Such energy order, in agreement with known
experimental work, is reversed by the adsorption of Co and Mn, which favour the
formation of hexagonal Nb-Nb clusters; this CDW structure is indeed allowed
from symmetry point of view but hidden in pure single layers because it is at a
higher energy. The other adsorbates, K and Ga, still favour one of the
triangular Nb-Nb cluster, while suppressing the other. We report how the energy
difference between such distorted structure varies with these adsorbates.
Furthermore, transition metals induce magnetism and favour the reduction of the
symmetry of the charge density distribution.
