Their relationship can be depicted in a variety of ways. It could be a professional relationship where they interact mainly in the context of village affairs. However, some fanfictions might explore a deeper bond, perhaps Kurenai being one of Naruto's closest confidantes. There could also be fanfictions where they have a bit of a rivalry in terms of their ninja abilities, which in turn adds an interesting dynamic to their relationship.
In some fanfictions, their relationship can be more of a mentor - mentee type in a way. Kurenai, being an experienced ninja, could offer Naruto, the relatively new Hokage, advice on handling certain situations within the village. Their relationship could also be portrayed as a friendship that has developed over time, sharing in the joys and sorrows of the village's growth and challenges.
Well, in fanfictions about Naruto, Kushina and Kyuubi, their relationships can vary greatly. Some fanfictions might focus on how Naruto inherits not only the Kyuubi's power but also some of Kushina's traits. For example, Kushina was known for her strong will, and Naruto might be shown to have an even stronger will because of her influence and the presence of the Kyuubi. The Kyuubi could be portrayed as a protector of Naruto in a sense, especially when it comes to threats that are related to Naruto's family history. And Kushina could be like a spiritual guide for Naruto when it comes to dealing with the Kyuubi's power.
In fanfiction, Naruto and Sasuke often have a complex relationship. Naruto is always trying to bring Sasuke back to the village. Sai, on the other hand, initially has a rather cold relationship with both due to his past and mission. But as time goes on, he becomes more involved in their circle. He might be used as a tool to understand Sasuke's actions or to help Naruto in his pursuit. Their relationships can be tweaked in various ways in fanfiction, depending on the author's take on the characters and the plot they want to create.
Some storylines might include Naruto as Hokage facing a threat that only Kurenai's special jutsu can help with. They could also have a story where Kurenai is wrongly accused of something and Naruto, as Hokage, has to prove her innocence. Or it could be a more light - hearted story where Naruto and Kurenai participate in a village - wide competition together, showing their different skills and personalities in a fun setting.
It could strengthen Naruto's relationship with Iruka. Since Naruto is the son of the fourth hokage, Iruka might see Naruto as an even more important part of the village and be even more protective. For example, he could be more involved in Naruto's advanced training.
His relationship with Sakura might be affected. Sakura has always seen Naruto as someone who would become Hokage. His refusal could make her question his long - term goals and how reliable he is in terms of the future of the village. She might be disappointed at first, but could also come to understand his perspective over time.
His relationship with Sasuke might be different. With Kurenai's influence, Naruto could be more understanding and patient, which might help him better deal with Sasuke's issues. His bond with Sakura could also change as he may approach her in a more mature way, having learned from Kurenai about relationships.
For one thing, the relationship between Kurenai and the Hokage (whichever one is in power at the time) would be put to the test. The Hokage might be initially hesitant about Kurenai's decision. But as Naruto grows under her care, it could lead to a stronger bond between Kurenai and the village leadership. Naruto's relationships with other ninja families would also be different. He might be more accepted into the social fabric of Konoha from a young age.
His relationship with Sasuke would likely become more of a partnership. They would work together to protect the village and the ninja world. With Sakura, Naruto might become more of a respected leader figure, and she could be one of his most trusted medical ninjas. And for Kakashi, Naruto would now be his equal in terms of leadership, and they would probably exchange ideas on how to better lead the village.
Her relationship with Sasuke would be very different. If she time - travels back, she might be able to approach Sasuke in a more mature way as a Hokage. Instead of just chasing after him out of friendship and rivalry, she could offer him real solutions to his problems and help him find his place in the village without leaving.
His relationship with his parents would be very strange. If he goes back to a time when his parents were alive, he would have to hide his true identity. But he could also get to know them in a way he never did. He might be able to change their fates as well, which would have a huge impact on his own life and the entire Hidden Leaf Village.