  We analyze the interplay of spin-valley coupling, orbital physics and
magnetic anisotropy taking place at single magnetic atoms adsorbed on
semiconducting transition-metal dichalcogenides, MX$_2$ (M = Mo, W; X = S, Se).
Orbital selection rules turn out to govern the kinetic exchange coupling
between the adatom and charge carriers in the MX$_2$ and lead to highly
orbitally dependent spin-flip scattering rates, as we illustrate for the
example of transition metal adatoms with $d^9$ configuration. Our ab initio
calculations suggest that $d^9$ configurations are realizable by single Co, Rh,
or Ir adatoms on MoS$_2$, which additionally exhibit a sizable magnetic
anisotropy. We find that the interaction of the adatom with carriers in the
MX$_2$ allows to tune its behavior from a quantum regime with full Kondo
screening to a regime of "Ising spintronics" where its spin-orbital moment acts
as classical bit, which can be erased and written electronically and optically.
