Well, in such a fanfiction, Naruto might be trained by someone else entirely. Maybe he gets trained by Jiraiya right from the start more intensively. This could lead to Naruto having a different fighting style, perhaps more focused on toad - related jutsus earlier on.
Another option could be Itachi. Although Itachi is from a different village and has his own complex situation, in a fanfiction scenario, he could secretly train Naruto. Itachi has extremely powerful jutsus and a deep understanding of the Sharingan. Training under him would give Naruto a very different perspective on power and combat, not to mention some insights into the Uchiha clan.
In such a fanfiction, Naruto might become extremely powerful under Kakashi's training. He could learn new jutsus faster and gain better control over his chakra. Maybe he'd also develop a closer bond with Kakashi, different from his relationship with Iruka or other characters in the original story.
Often, in 'naruto gets trained by kakashi fanfiction', Naruto will face various challenges during the training. These challenges could be physical, like enduring intense sparring sessions with Kakashi. Or they could be mental, such as understanding complex ninja concepts. Through these experiences, Naruto not only becomes more powerful but also gains a deeper understanding of himself and his ninja path. This might also lead to him forging a stronger bond with Kakashi, which could play a significant role in future plot developments.
Well, it could be that in this fanfic, Kakashi discovers a new potential in Naruto. He might train Naruto in some ancient and forgotten ninja arts. This would set Naruto apart from his canon self. Also, their relationship could be explored more deeply, like Kakashi becoming a father - figure to Naruto, and this emotional bond could influence Naruto's growth as a ninja.
In this fanfiction, Naruto's character development is multi - faceted. Physically, he becomes stronger and faster through the rigorous training. Mentally, he learns patience. Kakashi's training methods might include waiting for the right moment to strike or endure long periods of stealth. This teaches Naruto to be more patient in combat and in life. Emotionally, he matures. He may face setbacks during the training and learn to deal with failure in a more constructive way. Instead of getting frustrated and giving up, he uses it as a motivation to improve. All these aspects combined shape Naruto into a more well - rounded and capable ninja.
In this fanfiction, Naruto's relationship with his classmates would shift. Since he's being trained intensively by Kakashi, some might be jealous of the special attention he's getting. But others might respect him more for his growth. His bond with Shikamaru could also change. Shikamaru, being perceptive, would notice Naruto's newfound confidence and skills. They might end up collaborating more in missions or battles, with Naruto taking on a more leadership role in some cases.
Sasuke could be a side character. Since Naruto is getting special training from Kakashi, Sasuke might feel jealous or motivated to train harder himself. Sakura could also be there, perhaps she tries to learn from Kakashi's training methods to help Naruto better. Another potential side character could be Iruka, who might check on Naruto's progress from time to time and offer some words of encouragement.
He might gain better chakra control. Kakashi could teach Naruto how to precisely manage his chakra, allowing him to perform jutsus more efficiently and for longer periods. For example, Naruto could use his Shadow Clone Jutsu without exhausting his chakra so quickly.
Well, Kakashi might introduce Naruto to more strategic ways of fighting. For example, he could teach Naruto how to better analyze his opponents before attacking. Naruto, who was previously more impulsive, may start to hold back and look for the right moment to strike, like Kakashi does with his Sharingan.