She could be really energetic, just like Naruto. Maybe she has his blond hair and blue eyes too. And from Fuu, she might inherit some kind of unique chakra or special ability that makes her stand out among other ninja.
The daughter could also inspire a new generation. Young ninjas in the village might look up to her, especially if she has unique skills. This could lead to a change in the way ninjas are trained or how they view loyalty and family in the context of being a ninja.
She might inherit Naruto's strong will and determination. Since Naruto is known for his never - give - up attitude, their daughter could have that same tenacity. She might also have Yugito's unique kekkei genkai, which could make her a very powerful ninja in the fanfiction world. And perhaps she'd have Naruto's blond hair with some of Yugito's physical features.
She could be a very determined person. Growing up with Naruto as her father, she would have heard all about his struggles and achievements. So, she would likely strive to be as great as him. Maybe she'd be a bit of a rebel too, since she's not growing up in the traditional Konoha environment.
She could start off as a bit of a spoiled brat, used to all the perks of having a godlike father. But then, through a series of events like being kidnapped or facing a real threat to the village, she realizes she needs to grow up. So she starts training hard and becomes more independent.
In fanfiction, anything can be possible. Maybe some alternate universe scenario was created where Naruto and Yugito met under different circumstances. For example, if there were different political alliances in the ninja world that brought their two villages closer together. This could have led to more interactions between them and eventually a relationship that resulted in a daughter.
It would change the storyline in many ways. Naruto's focus would be more on his family with Kurenai and their daughter. He might not be as involved in some of the village politics or big missions. His time would be split between his family duties and his ninja duties. And his daughter could have unique abilities, either from Naruto or Kurenai, which could attract both good and bad attention in the ninja world.
It could change the relationships Naruto has with other characters. For example, his friends might be shocked at first but then become protective of his daughter. His enemies could see her as a new target or a way to get to Naruto.
It could be something like Sakura, after Naruto's friend. It would be a way to show his respect and friendship for Sakura. Or maybe something related to fire, like Kaen, since Kurenai is associated with fire - based jutsu.
One idea could be that the daughter has to hide her identity in the village that banished Naruto. She might inherit some of Naruto's unique abilities like his shadow clones. She could use these abilities in secret to help the villagers without them knowing she's related to the banished Naruto.