Tenten could develop a stronger sense of loyalty and friendship. When she decides to go after Naruto, she is putting her loyalty to him above the rules of Konoha at that moment. This journey could make her more empathetic towards others' situations and more determined to stand by her friends no matter what. For example, she might face opposition from some in Konoha for leaving to find Naruto, but she stands firm in her decision, which shows her growth in loyalty.
Naruto's character would likely become more independent. Away from Konoha, he has to rely on himself and the female Kyuubi. He might become more cautious as he no longer has the safety net of his village. His view of friendship could also change. Since he's with the female Kyuubi, he might develop a deeper understanding of different beings and their motives.
Their relationship could start as comrades on a mission. As they leave Konoha together, they'll have to rely on each other. Naruto's sunny personality might gradually break through Samui's more reserved nature. They could start sharing their pasts, with Naruto talking about his lonely childhood in Konoha and Samui sharing about her life in the Cloud Village. This sharing would bring them closer, and they might develop a deep friendship at first, which could potentially turn into something more romantic as they face more and more challenges together.
One possible plot could be that Naruto leaves Konoha due to some misunderstanding. Tenten, being a friend, decides to go after him to bring him back. Along the way, they face various challenges together, which makes them grow closer and understand each other better. Maybe they encounter a group of rogue ninjas who are after Naruto's power. Tenten uses her weapon skills to protect Naruto, and Naruto starts to see Tenten in a new light.
Naruto's character would likely be more independent. Without the structure and support system of Konoha, he would have to rely on himself more. He might be more distrustful of large organizations, having not grown up with the sense of community that Konoha provides.
Naruto would likely become more independent. Without his mother, he'd have to rely on himself more. He might also become more reserved as he has this emotional wound. His relationships with others, like Iruka Sensei, could deepen as he looks for that parental support elsewhere.
Naruto becomes more self - reliant. When he's out training on his own, he has to learn to make decisions without the help of others. He also gains a broader perspective as he meets different people during his travels. This exposure to new cultures and ways of thinking in fanfiction enriches his character. He starts to understand that there are many different paths to power and that he can learn from everyone. His ninja skills improve, of course, but his mental and emotional growth is just as significant.
Naruto's character would likely be more confident. With Kushina by his side, he'd have someone to constantly affirm him. He might not have the same desperate need for recognition from the village. His skills could develop faster as Kushina could train him. He'd also have a better understanding of his Uzumaki heritage earlier, which could shape his identity in a different way.
Naruto's character could become more cynical. Constant hatred from the village might make him question his loyalty to Konoha. He might start to keep more to himself and be less trusting of others.
Sakura would probably be very worried. She has always cared about Naruto deep down, so she might be constantly trying to find a way to bring him back. Kakashi, on the other hand, would likely understand Naruto's reasons to some extent. He might be sad but also respect Naruto's decision. As for Sasuke, if he is in the village at the time, he could be conflicted. He and Naruto have a complex relationship, and Naruto's leaving might make him realize how much Naruto actually means to him.
Their relationship could start with mutual respect. Naruto respects Tenten's dedication to her weapon - based ninjutsu, and Tenten respects Naruto's strength and determination. They might start training together more often, which would lead to them spending a lot of time together. This time together would allow them to open up to each other about their pasts, their fears, and their hopes for the future. As they grow closer, they would start to develop feelings for each other, and these feelings would eventually lead to their marriage.