You'll just have to call Sunpass from the airport with the rental car info each time before you use it. In all honesty we forgot to do so several times and never had a problem.
The Sunpass is registered to YOU not a specific car, and you can use any address, it doesn't need to be a Florida address. But they do want to have the tag number of the car it's being used on. You can have multiple cars registered to a single Sunpass.
You do need to decide if the cost of purchasing the transponder ($25) is worth it to you.
Anne