The main character is Percy. But we can't forget about other demigods. They could be there in the background, cheering Percy on or being afraid of the consequences of his actions. The gods, especially those who have a direct connection to Percy like Poseidon his father, will be key characters. And there could be some minor gods or goddesses involved too if the fanfiction explores different aspects of the godly realm and Percy's grievances against them all.
Percy is the central figure for sure. The gods, like Hades, might be there too if the story involves issues related to the Underworld. Grover could also play a role. He is Percy's friend and might be there to support Percy when he yells at the gods, or his experiences with the gods could be part of what drives Percy to yell. Chiron, the centaur, could also be a character as he is a mentor to Percy and could have some influence on the situation.