But it has to be a chthonic deity, and the usual IAU Minor Planets Committee rule is that moons should be mythologically related to their primary's name.

Excellent. I assumed that was a courtesy, not a rule; I am pleased to discover otherwise.

Thank goodness the outer solar system is more mythologically diverse than it used to be...

If there are not already objects named Nergal, Ereškigal, Namtar, there totally should be.