One possibility is that Naruto, being neglected by the village, would be full of pent - up anger and a thirst for recognition. Kaguya's training could focus on unlocking hidden powers within him. For example, she might teach him ancient jutsu that no one in the village knows. This could lead to Naruto developing a unique fighting style that combines his Uzumaki heritage with Kaguya's otherworldly knowledge.
Well, in such a fanfic, Naruto might gain some extremely powerful and unique abilities. Kaguya being his trainer could mean he'd learn ancient and forbidden jutsus. Maybe he'd also gain a deeper understanding of the chakra and the origin of the ninja world.
Well, Naruto would likely gain some really unique and powerful abilities. Since Kaguya is extremely powerful, she could teach Naruto some ancient and secret techniques that are not known in the normal ninja world. Maybe he'd learn more about the origin of chakra and how to manipulate it in ways he never thought possible.
One possible plot could be that Naruto, under Kaguya's training, gains godlike powers at an accelerated rate. He might learn ancient and powerful jutsu that were once exclusive to Kaguya. This could lead to him facing new and extremely powerful enemies, perhaps even threats from other dimensions. With Kaguya's guidance, Naruto could also gain a deeper understanding of the chakra and its origins, and use this knowledge to reshape the ninja world for the better.
One potential antagonist could be those who fear Naruto's new - found godlike powers. There might be ninja from other villages who see Naruto as a threat to the balance of power. Another could be remnants of Kaguya's old enemies who resurface, seeing Naruto as a continuation of Kaguya's influence and wanting to stop him. Also, there could be dark forces within the ninja world that want to corrupt Naruto's new powers for their own evil purposes.
His understanding of the ninja world would expand. He might become more cautious and calculating in battles, as Kaguya's training could expose him to different strategies. Also, he could develop a more solemn side to his personality, considering Kaguya's own complex nature and the heavy knowledge she might share.
Well, it could be that Naruto, being neglected in the village, is noticed by Shisui. Shisui sees Naruto's potential and decides to train him in stealth and combat skills. Naruto then starts to grow stronger under Shisui's guidance, and eventually surprises everyone in the village with his newfound abilities.
Well, the plot could involve Naruto being overlooked in his own village, so he somehow ends up in the world of One Piece where Zoro takes him under his wing. Zoro might start training Naruto in his unique sword - fighting style, which Naruto could adapt to his own ninjutsu - based combat. For example, Naruto could learn to use his chakra to enhance the speed and power of sword strikes, similar to how he uses it for his shadow clones or rasengan.
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.