The game has a religion system with deities that already exist, this means that while you as a person could RP some other faith, NPC's wont't acknowledge it and you can't gain any bonuses like you do from the other faiths.
So really, there isn't much point in doing that. There might be a chance to re-interpret the teachings of a god, so while you still follow the faith you do so in a different manner, eg: Kypiq and Janoans both believe all animals have a soul, the Janoans believe that if you consume them you gain their soul and strength, the Kypiq don't and believe they should be protected.
Both start from the same premise then interpret it very differently.
(I apologies if I made a mess of that comparison, Faeden isn't my strong suit, but it was the best I could think of).