Regarding the god of death convo a couple of pages back the term you're looking for is "psychopomp".
A psychopomp is a god/spirit/deity/random-thing who's job is to collect the souls of the dead and carry them to the afterlife. Generally, it's not that they actually kill people, mortality manages to take care of that, they just clean up after it's happened.
Some examples would be Anubis (Egyptian), Thanatos ((Greek), not thanos), Valkyries (Norse), Shinigami ((Japanese), I think not sure about them), the grim reaper ((western/European) changes depending on characterisation)
It's a distinctly separate thing from gods that rule over the afterlife (the place) such as hades (greek), pluto (roman), Osiris (Egyptian)
Also of note is that actually judging the souls of the dead is often done by something other than the gods. Rather than being dependent on the random, changeable whims of a deity (because would you trust Zeus to take that seriously) they often had some kind of solid mechanism or process to it. Makes it easier to know and follow the rules I suppose.
Egyptians weighed your heart against a feather with evil deeds weighing your heart down, the greeks had a panel of historical figures who determined where you ended up, not sure for the Norse (much of it is vague because we don't really have any good pre-Christian sources) though I believe it has something to do with where and how you die
I can't see Taylor ending up with ruling the underworld as a domain, a common trend with them is that they're kinda stuck there ruling their domain, but I suppose we could end up with foxes in a psychopomp role. Get into an accident only to have a cute fox pop up and inform you that you're dead and lead you to the afterlife.