Characters like Gaara may also appear. He could be an ally king to Naruto, and together they form a powerful alliance against common enemies. The Akatsuki members might be the antagonists in some fanfictions, trying to overthrow Naruto's kingdom or steal valuable resources from it.
The main character is Naruto, no doubt. But other characters from the Naruto universe can also be main players in these fanfictions. For example, Jiraiya could make an appearance. He might have known about Naruto's potential as the 'King of Nature' all along and left some clues or teachings for Naruto to discover. And then there are the various tailed beasts which could have a special connection to Naruto as the 'King of Nature'.
Love and loyalty are common themes. Naruto as a king often has to face many challenges, and Hinata's loyalty to him and their growing love is a central focus. For example, in many fanfictions, Hinata stands by Naruto through political unrest.
In these fanfictions, a very common element is Naruto's enhanced strength and abilities. He may be able to traverse between the living world and the afterlife at will. His moral code might also be put to the test as he rules over hell. There could be a lot of focus on his interactions with the denizens of hell, be they former foes or new characters created specifically for the fanfiction. Moreover, there may be a backstory about how he came to be the 'godlike naruto king of hell', which often involves some sort of epic journey or transformation.
Often, you'll see Hinata as part of the harem. Her shy nature contrasts with Naruto's more bold Mokuton - using self. Sakura might also be there, adding an interesting dynamic as she has her own history with Naruto. And then there could be some original characters created just for the fanfiction to add more flavor to the harem.
Hinata is also often paired with Naruto. In a fanfiction, Hinata might notice Naruto flinching and use her gentle and understanding nature to comfort him. She could be the one to figure out what is wrong and support Naruto through his difficult time, which would further develop their relationship in a sweet and tender way.
Well, Naruto himself is obviously a central character. Then there are often female characters like Sakura, Hinata, and Ino. Sakura might be written as more aggressive in her pursuit of Naruto in the harem scenario. Hinata could be the shy but very loyal one, and Ino might bring a bit of sass and competition to the group.
Sakura could be a common supporting character. She might be jealous of Hinata's relationship with Naruto at first, but then comes to accept it and even helps them in the game - related adventures. Shikamaru could also be there. His intelligence would be useful in devising game strategies for Naruto and Hinata. Kiba and Akamaru might be their opponents in some game battles, adding an element of friendly rivalry.
Obviously Naruto himself is the most common. His friends like Sasuke and Sakura also often appear. Kakashi - sensei might show up too, perhaps to give Naruto some sage advice during his bath time. And Jiraiya could be there as well, since he was Naruto's mentor and had a close relationship with him.
One common element is the exploration of the bonds between characters. In Naruto, friendship and rivalry are strong themes, and fanfictions often expand on these. For example, the relationship between Naruto and Sasuke is a popular one to explore, whether it's about their reconciliation or their epic battles.
One interesting 'Naruto is a King' fanfiction could be where Naruto rules a hidden village in a completely new way. He might introduce reforms that change the power structure and how shinobi are trained. For example, he could focus more on diplomacy and trade, making the village prosperous not just through combat strength.