Well, all the regular Naruto characters would still be there. Sasuke could be a major character. He might be initially skeptical or even jealous of Naruto's new identity. Kakashi could also play a role, perhaps trying to help Naruto control his new powers. And from the Shiva side of things, Nandi, Shiva's bull, could be a character. He could act as a protector or a guide to Naruto, teaching him about Shiva's ways and powers.
Well, surely Hinata would be there. As Naruto's wife, she would support him in his role as Uzukage. Maybe Boruto and Himawari would also be involved, learning about their Uzumaki heritage from their father. And there could be some other Uzumaki clan members who have been in hiding and now come out to help Naruto lead the village.
There could be characters related to Luna. Maybe Luna has some friends or family members who play important roles. Also, the regular Naruto characters like Sasuke and Sakura would still be there, but their relationships with Naruto might change due to his new identity as Luna's son.
Sasuke could be in it. He might be initially skeptical of Naruto's new power but then see its potential in combat.
In this fanfiction, Naruto's abilities would be significantly enhanced. His chakra reserves, which are already considerable as a ninja, could be limitless or close to it as the son of Shiva. He might be able to perform new jutsu that combine ninja techniques with Shiva - related powers. For instance, he could create illusions based on Hindu mythology that are not only visually deceiving but also have a spiritual impact on his opponents. His physical endurance would also be off the charts, allowing him to fight for long periods without tiring.
Princess Luna herself would be an important character. Also, characters like Sasuke could be there, and their relationship with Naruto might change because of his new heritage.
One character could be Jiraiya. He could have known something about Naruto's true heritage all along and be the one to finally reveal it to Naruto. From the Greek side, Triton, Poseidon's son in mythology, could be a character. He could either be a rival or an ally to Naruto. In the ninja world, Shikamaru might be involved. His intelligence could be used to help Naruto understand and strategize with his new powers, especially when dealing with any threats that come his way because of his connection to Poseidon.
Obviously, there would be the queen vampire, his mother. She could be a powerful and mysterious figure, perhaps with her own motives and plans for Naruto. There might also be some vampire elders or nobles who play a role in Naruto's life, either guiding him or trying to use him for their own purposes.
The Daimyo of Wave himself would be a main character for sure. Also, his guards or advisors who have a say in the running of Wave. Maybe a young heir to the Daimyo who is being groomed to take over and has his own ideas about the future of Wave.
Sasuke could be a main character. He might be initially interested in the dragon egg for its power but then his relationship with Naruto over the egg could change. Maybe they start as rivals again, but then realize they need to work together to protect the egg.
Sakura could be there. As Naruto's friend, she might be the child's doctor, always ready to heal any injuries. She could also give parenting advice to Naruto based on her medical knowledge.