Indeed it's quite stupid. Any alternative catchy name for the concept?
Catchy like vagrant but perhaps a bit insensitive (unless it was used to highlight the plight of the homeless).
Less catchy - Poste Restante or General Delivery
"Don't care where it runs, don't want to manage it, I want to pay only for when I actually use it, thanks for managing it, here's some extra cash for the effort"
But you can only apply that metric if you remove the end users from actually touching the machines (virtual or real).
This is the "less" in serverless.
Turns out that this is also something people want: not having to be on the hook for actually administering machines, installing security patches etc etc.
So managed (platform as a) service + fine grained billing
Managed service