LEO will be worthless soon enough.

https://outerspaceinstitute.ca/crashclock/

Technically it is a limited resource, since there is only a finite volume. But we're nowhere near close to any notion of it being "full." Efficient rent would be approximately zero.

To whom would they pay 'rent'? What would be done with the money?

Don't go there, it leads to nothing but more waste, abuse and corruption. If it becomes necessary there can be some form of arbitrage in how LEO is used, we're not there yet though. Maybe something like the auctions for bandwidth for mobile operators but again, where does the money go? If institutionalised it will just turn into another slush fund for whatever interests, many of them corrupt or nonsensical, to drain.