If you are looking for a rental car inside the Civitavecchia port: You will not find it, because there is not an internal car rental.
There are three companies, just outside the harbor, (10 min by walk)
AVIS. Addr: Via XVI Settembre 6. Tel 0766500336
EUROPACAR. Addr: Via Tarquinia 19. Tel 0766 502464
HERTZ. Addr: Via della Repubblica 10A. Tel 0766 22998