It could change his relationship with his enemies too. Enemies might be more hesitant to attack him, not knowing what the mouths on his hands can do. Some might be so freaked out that they avoid him altogether. His relationships with his sensei, like Jiraiya, would be interesting. Jiraiya would likely be excited to study this new phenomenon and help Naruto figure out how to use it to his advantage. And Naruto's new 'hand - mouths' could also bring him closer to some characters who are interested in the strange and unusual in the ninja world.
It would likely strengthen his relationship with Kakashi. Kakashi, being Naruto's teacher, would be intrigued by this new power and help Naruto train and master it. His respect for Naruto would grow as he sees Naruto handle such a powerful and unique summon. With Sasuke, it could be a source of both envy and a reason for him to re - evaluate Naruto. Sasuke might initially be jealous of Naruto's new power but later realize that they need to work together, especially if the dragon summon is crucial in fighting a common enemy. As for his friends like Shikamaru and Choji, they would be in awe of Naruto's dragon and it would make them more eager to fight alongside him, seeing him as an even greater asset in battles.
His relationship with his teachers could change too. Kakashi might have to develop new training methods for Naruto to master this kekkei genkai. Iruka would be very supportive as always, but also a bit worried that Naruto might attract more dangerous enemies with this new power. And with the other ninja villages, they might view Naruto with more caution or respect depending on how powerful his kekkei genkai is.
With his friends like Sakura and Kakashi, they might be initially confused but then supportive. Sakura could be worried that Naruto is getting involved in something dangerous related to the moon, but also trust that he knows what he's doing. Kakashi, on the other hand, would likely be more intrigued and offer his wisdom and guidance as Naruto explores this new aspect of his life.
It might actually strengthen his relationships in some ways. His friends could see him as an even more powerful ally. Naruto, with these new powers, could protect them better. Sakura, for instance, would feel safer around him and this could lead to a deeper bond of trust between them.
Well, it might make his relationships more complex. His friends could be both curious and a bit wary at first. For example, Sasuke might see him as even more of an oddity, which could either drive them further apart or make Sasuke more protective in a strange way. Sakura might be more motherly towards him, trying to take care of him because of his new features.
Naruto's relationship with his teachers could be different too. Kakashi, for example, would need to adjust his training methods for Naruto. He would have to help Naruto master the Byakugan while still maintaining his existing skills. And Naruto might also have new interactions with other powerful ninjas in the village or from other villages, as they are curious or intimidated by his new - found Byakugan - related abilities.
His relationship with Sasuke would be greatly affected. If Naruto could control time, he might be able to show Sasuke what the future could be like if they worked together instead of being enemies. This could potentially heal their fractured relationship much faster. With space - control powers, Naruto could quickly reach Sasuke whenever he was in trouble, strengthening their bond of friendship.
This second personality could have a significant impact on Naruto's relationship with the tailed beasts. Since Naruto has a connection with the Nine - Tails, a second personality could disrupt that bond. The Nine - Tails might react differently to this new personality, either seeing it as a threat or an opportunity. And when it comes to his international relationships, like with Gaara from Sunagakure, Gaara would be very curious and perhaps a bit worried. Their shared experiences of being outcasts might be overshadowed by Naruto's new personality, and Gaara would have to decide how to interact with Naruto now, whether to approach him with caution or try to help him like he once did when Naruto was in trouble.
As for his relationship with Kakashi, Kakashi would likely see the potential in Naruto's ink bloodline limit and start to train him in new ways. He could help Naruto develop his ink - based jutsu and incorporate it into his overall fighting style. This would strengthen their teacher - student relationship as they explore this new aspect of Naruto's power.
It would change his relationships a lot. His friends like Sakura and Sasuke would be both intrigued and maybe a bit worried. Sasuke, who has his own Sharingan, might see Naruto as more of a rival now. Sakura would be concerned about the risks of the implantation. And his relationship with Kakashi would also shift. Kakashi could help Naruto better understand and control the Sharingan, creating a stronger bond between them as teacher and student.