One idea could be Hiruzen teaching Naruto some of the most secret and powerful jutsu in the village. For example, a special fire - style jutsu that was once used by the First Hokage. This would give Naruto an edge and also show the bond between him and Hiruzen. Another plot could be Hiruzen training Naruto in the art of political leadership. Since Naruto is destined to be a great leader, Hiruzen could impart his wisdom on how to handle different clans and political situations within the village.
Naruto would become more well - rounded. With Hiruzen's training, he'd gain more discipline. In the original, Naruto was a bit of a wild card. But under Hiruzen, he'd learn to control his impulses better. For example, in battles, he'd think more strategically instead of just charging in.
Maybe Naruto is put in a situation where he feels that Hiruzen's way of handling things is the best option. For instance, if there is a major crisis in the village that requires a more traditional and experienced approach, Naruto might choose to act like Hiruzen. Also, he could be influenced by the stories he has heard about Hiruzen and wants to fill his shoes in a way.
Perhaps in this fanfiction, Naruto has some sort of special power or transformation that he unlocks just in time to face Orochimaru. It could be related to his Nine - Tails chakra in a new and unique way. He uses this power to break through Orochimaru's defenses and save Hiruzen. Naruto might also use his knowledge of Orochimaru's weaknesses that he has learned either from Jiraiya or from his own past encounters with Orochimaru's minions.
In a 'naruto adopted by hiruzen fanfiction', the plot could involve Naruto having a closer bond with the older generation of shinobi. Hiruzen would surely introduce Naruto to his trusted comrades. Naruto could learn unique jutsu from them. Also, his growth as a ninja would be different. Instead of seeking attention through pranks, he might focus more on living up to Hiruzen's name. His relationship with Sasuke could also be affected. Maybe they would become rivals in a more positive way, with Naruto having a stronger sense of family and purpose because of Hiruzen's influence.
Yes, in certain fanfictions Naruto hates Hiruzen Sarutobi. Fanfiction often takes the original characters and storylines and twists them. Maybe the writer of such a fanfiction thought that Hiruzen's actions, like not fully protecting Naruto when he was a child, could lead to Naruto having negative feelings towards him in this alternate take on the story.
In the fanfiction, Hiruzen might raise Naruto properly by providing a stable living environment. He could ensure Naruto has a decent place to live, enough food to eat, and warm clothes. This basic care is fundamental for Naruto's growth.
One interesting story could be about Hiruzen mentoring Naruto in some unique jutsu that was long forgotten. This would show a different side of their relationship, focusing on the transfer of knowledge from the old to the new generation.
Perhaps Hiruzen is being influenced by some dark force or a hidden group within the village. They convince him that Naruto, with the Nine - Tails inside him, is too dangerous to be left unchecked. So, Hiruzen, in a moment of weakness, decides to betray Naruto. He could secretly arrange for Naruto to be sent on dangerous missions alone with the intention of getting him killed. Naruto, being oblivious to this at first, later realizes what's going on and has to fight not only against external enemies but also against the betrayal of his own village leader.
In this fanfiction, perhaps Hiruzen realizes Naruto's potential much earlier and decides to train him privately. He might take Naruto on secret missions to build his experience and confidence. This would not only strengthen Naruto's skills but also their bond, which could have a huge impact on the village's future.