Lupa herself would be a major character. She's the one who has a special connection to Percy in this story. She could be guiding him, testing him, or having her own motives that are intertwined with Percy's journey.
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.
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.
A prevalent theme is isolation. In many fanfictions, Percy feels alone because of his strange heritage. He doesn't quite fit in with the normal demigods. Also, the theme of destiny often comes up. He has a special destiny due to his parents that he is constantly striving to fulfill.
I've read a fanfiction where Percy is the son of Lupa and Chaos and it focuses on his relationships. 'Percy's Bonds' is the name. It shows how his different heritage affects his friendships and romances, and how he has to come to terms with who he really is in the context of his relationships.
One interesting plot could be Percy having to prove himself to Lupa's pack in a series of dangerous trials. Maybe he has to hunt a mythical beast that has been terrorizing the pack's territory.
One common theme is identity. Since Percy has two very different divine parents, he often struggles to figure out who he really is in fanfictions. Another theme is power. With the combined powers of Lupa and Poseidon, his power levels and how he uses them are often explored. Also, acceptance by his peers is a big theme as they may view his dual heritage as strange or overpowering.
Obviously Naruto would be one of the main characters. And since it's about him being the son of Lupa, Lupa would also be an important character, even if she might be an original creation for this fanfiction.
His relationship with Annabeth would be severely strained. Annabeth, who has always known Percy as Poseidon's son, would be confused and a bit distrustful. She might think Percy has been lying to her all this time. His friends at Camp Half - Blood would also be divided. Some would be scared of his new powers and his connection to Tartarus, thinking he could be a danger. However, some might be more understanding, especially those who have faced their own identity crises. His relationship with the gods would also change. The gods who were once somewhat friendly or at least neutral towards him might now see him as a threat. Zeus, for example, would be extremely wary of Percy's Tartarus - related abilities.
Another important character could be Chiron. He, as the centaur mentor, plays a crucial role in guiding Percy. He might be the one to first discover Percy's ice powers and then help him understand the implications of being the Son of Ice. There could also be villains, such as a dark wizard who wants to steal Percy's ice powers for his own evil purposes.
In addition to Percy, there could be new characters created specifically for this fanfiction. Maybe a dragon trainer or someone from an ancient dragon - associated clan. They could guide Percy in his journey of self - discovery regarding his dragon heritage. And of course, we can't forget the villains. There might be some dark demigods or creatures that oppose Percy because of his newfound powers.