Closing IFR flight plan at uncontrolled field

It depends.

They tell you who to call by phone when they approve you to switch
frequencies.

If the last facility you were talking to was a civilian TRACON, they
usually want you to call them. If it was military or an ARTCC, they
usually want you to call FSS.

.... but that can change, even at a given airport.

If I were on the ground and wasn't sure who call, I'd call FSS first.
They'd either cancel IFR for me or tell me who to call.