The slug is the part of the URL after places/, so in https://www.inaturalist.org/places/forest-below-pohutukawa-bank, the slug is forest-below-pohutukawa-bank. I don’t know how or why slugs sometimes get set to null, but if you have edit privileges on a place, you can change the slug.
To do this, go to the edit page for your place.
Then set the Display Name to the name you would like for your slug (it will automatically be changed to lowercase, spaces replaces with dashes, etc.).
Then, because there is a small bug, you also need to change the Name in order to force the slug to update. Any change is fine, and you can change it back afterward.
When you save the changes, the slug should immediately update.