Since no one else has mentioned it, in the UK (and other Commonwealth countries) these are called "peppercorn" rents: https://en.wikipedia.org/wiki/Peppercorn_(legal)
On my previous house, we had a leasehold of just our garage, oddly, with a peppercorn rent of £1 a year. Being young and innocent, I did ask whether I actually had to pay this, but my solicitor just laughed.