One possible plot could be that Naruto gains a whole new family structure. Hiashi might train Naruto in the ways of the Hyuga clan, which could make Naruto an even more formidable ninja. He would also be exposed to the Hyuga's strict traditions and might have a different view on the ninja world. Maybe he'd form a closer bond with Hinata earlier as they'd be siblings in this scenario.
Well, if Naruto was adopted by Hiashi, his life would change drastically. Naruto, who was always an outcast in the village, would now be part of one of the most respected clans. Hiashi could help Naruto control his chakra better using Hyuga techniques. Also, Naruto might have to deal with the internal politics of the Hyuga clan. He could use his positive attitude to change some of the more rigid ways of the clan, and perhaps bring a new sense of unity among the Hyuga members.
One interesting plot could be that Hiashi discovers Naruto has some hidden connection to the Hyuga clan. This would make Hiashi take a special interest in Naruto, and he might start training Naruto in Hyuga - related skills.
His relationship with Hinata would be completely different. Instead of a potential love interest, she'd be his sister. His relationship with Neji might also change. Neji might be less hostile towards Naruto as they'd be part of the same family. Naruto would also have a new relationship with Hiashi as his adoptive father, and he'd have to follow Hiashi's rules and guidance.
Well, it could be about Naruto growing up in the Hyuga clan. Maybe he discovers his true parentage early on and has to deal with the expectations and politics of the clan. He might learn the Gentle Fist technique in a different way than Neji or Hinata.
Maybe Hiashi adopts Naruto because he realizes that Naruto is a key to uniting the village. As Naruto becomes part of the Hyuga family, he starts to influence the clan's view on outsiders. He might introduce some new training methods that he learned from Jiraiya. Naruto could also have a role in protecting the Hyuga's secrets, like the Byakugan. He would grow in a different environment, and this would change his relationships with characters like Sasuke and Sakura in new and unexpected ways.
If Naruto was adopted by Kyuubi in fanfiction, it could lead to a completely different Naruto. He might be more confident earlier on. Since Kyuubi is a very powerful being, Naruto could be trained in unique ways. For example, he could learn how to harness Kyuubi's power more effectively without the need for the traditional methods of suppressing and drawing on the fox's chakra. This would change his relationships with his peers too. He might be seen as an oddity, but also as someone with great potential.
Well, it could be that Konan finds Naruto alone and decides to take him in. Maybe she sees his potential and wants to protect him from the harsh world of shinobi. She could teach him some of her own unique skills, like her paper ninjutsu. And Naruto, with his positive attitude, might influence Konan in return, making her more open and hopeful.
In a 'naruto adopted by sesshomaru fanfiction', the plot could start with Naruto being exiled from Konoha for some false accusations. He then stumbles into Sesshomaru's territory. Sesshomaru, initially indifferent, realizes Naruto's strong will which reminds him of his own. So he adopts Naruto. Naruto then has to adapt to the new world of demons and yokai, while also trying to find a way to clear his name back in his own world.
Well, one possible plot could be that Naruto, being adopted by Madara, is trained in ancient and powerful Uchiha techniques from a very young age. This would make him an even more formidable ninja early on. He might also gain insights into the Uchiha's history and grudges, which could influence his views on the village and its politics.
If Naruto were adopted by Fugaku, he'd likely be exposed to the Uchiha's Sharingan secrets earlier. This could give him an edge in battles and a different perspective on his own powers. He might also face more political intrigue within the Uchiha clan. With Fugaku as his father figure, Naruto could become more reserved and calculating, rather than his usual impulsive self. His relationship with the village might also be different, as the Uchiha had some underlying tensions with the rest of Konoha.
In this fanfiction, perhaps Naruto is adopted by Ibiki after a particularly dangerous mission where Ibiki realizes Naruto's potential but also his need for a proper family. Ibiki could train Naruto to control his emotions better, which is something Ibiki is good at due to his work in interrogations. Naruto would grow up with a new sense of purpose and family, and might even use Ibiki's teachings to become a more well - rounded shinobi, for example, using interrogation - like skills to gather information during missions.