I have the cloud saves enabled. I can rent other pawns but mine has never been rented.
It's possible that your pawn is currently being rented but hasn't been released yet.
Or your pawn just isn't considered interesting to whoever runs across it.
I was under the impression that the gifting and the system to earn RC were broken. Having said that I haven't really wandered far from gran soren yet so neither my pawn nor I have good equipment so I don't really expect her to be rented anyway.