Death's new name? Bill Door. In Eric, Eric and Rincewind decide that the bill is "what you get when there's nothing left and everything's been used up." What do you get when there's nothing left and everything's been used up? Death.
I should say that Bill DOOR is a rather obvious reference to Bill GATEs, but it might only be me...
Or perhaps "Bill Door" makes a pun on "Builder," which is the opposite of Death's usual job.
A door is a transition. Death is also a transition.
There's a philosophical statement: "Death is only a door."
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