Some of the more malevolent spirits or monsters from the Underworld could also be antagonists. They might resent Percy for being Hades' adopted son and try to undermine him. For example, a powerful undead general who believes he should be the one favored by Hades instead of Percy.
One idea could be Percy having to deal with the stigma of being associated with Hades in the demigod world. He might face distrust from other demigods who are scared of Hades' reputation.
One idea could be Percy having to mediate between Zeus and Hades during a major feud. Since he's the son of both in this fanfiction, he has a unique connection to them. He could use his powers and his knowledge of both of their domains to try and broker peace.
In this fanfiction, there might be a lot of focus on Percy's relationship with the other wolves in Lupa's pack. He could learn their ways of survival, their hierarchy, and how to be a part of their community. This would be a great way to explore his adaptability and growth.
One common theme is the struggle with identity. Since Percy is usually the son of Poseidon in the original series, making him the Son of Hades in fanfiction often leads to him dealing with a new sense of self. Another theme is power and its consequences. Hades has a lot of dark and powerful abilities, so fanfictions might explore how Percy copes with having access to such powers.
Annabeth Chase might also be an ally. Her intelligence and strategic thinking could be valuable assets for the son of Hades. She could help him plan his moves, especially when dealing with the complex politics among the demigods and gods.
Well, of course, Percy Jackson himself often makes an appearance. He could be a mentor figure to the adopted son, guiding him through the ropes of being a demigod. Annabeth is also common, perhaps helping the adopted son with her wisdom and knowledge of the mythological world.
The setting of the story might shift a bit. Instead of always being at Camp Half - Blood or on quests related to the Greek gods, Percy could be in the territory of the wolves. There could be new threats and challenges there, like rival wolf packs or ancient enemies of Lupa. And all these elements would make for an exciting and different take on the Percy Jackson universe.
One interesting plot twist could be Percy finding out he has a hidden power related to Hades' realm that he didn't know about before. Maybe he can control a special type of underworld creature that no one has ever seen. Another could be Percy having to face off against a false heir to Hades' throne who is trying to frame him for crimes in the underworld.
Obviously, Percy Jackson himself is a main character. He's the one with the new identity as the son of Hades. Nico di Angelo could also be a major character as he has a strong connection to Hades already. And Annabeth Chase would likely be involved too, as she's Percy's close friend and often by his side in adventures. There could also be some new characters created specifically for the fanfiction, like a powerful Underworld spirit that becomes Percy's guide or an enemy within the Hades - influenced areas.