I have a deck about 15 years old that is structually sound. I am contemplating replace the deck surface with composite material. The frame is pressure treated lumber. It currently has a single rim joist. Should I be adding a second rim joist as part of this project?

If the rim joist is simply a rim joist, and not acting as a beam or girder, there is no reason to double it.

Sometimes another board is nailed over the rim joist for decorative reasons, but a true rim joist does nothing but tie the ends of the joists together and keep them from rotating, so there is no reason to double it.