I am renting a camper van for a road trip through Italy. Is it ok to stop at a rest area to sleep over? Do you just find a parking space or have to tell someone? Is it legal? What are the rules? Is it generally safe/patrolled?
You will find plenty of free public parking lots where you can spend the night in.
As long as you don't open tends or similar and you just sleep, there is an high probability that no one will come at you complaining. Unless there is a specific sign that tells you it's forbidden.
Moreover, usually in average size towns the parkings spots that you have to pay for during the day are free during night until 8 am. You can park also there for example.
(Another story is the safety of some isolated parking lots. For example large mall parking lots are not very populated during night, so safety could be an issue for someone sleeping inside a vehicle)
Wild camping with a camper van is legally the same as camping with a tent. That being said, wild camping is not allowed in most countries within Europe.
A quote from this answer:
Italy: It doesn't seem to be tolerated, in fact most sources I can find seem to say it's explicitly banned in many places.
As long as you don't finde a place where camping is specifically allowed, or stay on private property (with permission of the owner of course) you can expect it to be forbidden.
Living in a Van/Camper/Car is actually a big thing, especially in the US, Europe, Australia, etc.
So, in this case, your best best is to Bing/Google things like 'van life italy', 'stealthing italy' or 'boondocking Italy'.
You'll get lots of Blogs, Vlogs, YouTube Channels talking about every aspect including non-rest stop places.