Well, perhaps Naruto finds the cat girl alone and injured. He decides to take her in out of his kind heart. She might start to learn ninja skills from Naruto and his friends, and there could be a lot of comical moments as she tries to adapt to the human world while still having her cat - like behaviors.
It could be a group of rogue ninjas who are after the cat girl for some special power she might possess. They see Naruto as an obstacle in their way to get to her.
The child could be an orphan from a small, destroyed village that Naruto comes across during one of his missions. This child might have lost their family to a powerful enemy and Naruto feels a sense of responsibility to take them in.
Well, it could be about Haku taking Naruto under his or her wing in a fan - created story. Maybe it explores how Haku's character, with his or her unique abilities and backstory, influences Naruto's growth and development. It might also show how their relationship changes over time, perhaps leading Naruto to learn new skills or gain a different perspective on life.
Iruka - sensei is a character that can show up. Since he was important in Naruto's life, he could play a role in the girl's upbringing too. He might help with her education in the ninja academy. Also, the Akatsuki members could be antagonists in some stories. Their actions might force Naruto to protect the girl more fiercely, and this would drive the plot forward as Naruto battles against them to keep the girl safe.
Well, it could start with the little girl being an orphan from a destroyed village. Naruto, having experienced similar pain, feels a strong connection. He adopts her and as she grows up, she becomes a source of pride for Naruto. She might also have some unique abilities that Naruto helps her develop while also protecting her from those who might want to use her powers for bad.
In some 'naruto adopts girl fanfiction', the girl might be an orphan from a war - torn area. Naruto, having known the pain of being alone as a child, takes her in. He helps her overcome her trauma by sharing his own experiences. For example, he could take her to Ichiraku Ramen and introduce her to his favorite food, creating a bond over simple pleasures. As she grows, she starts to show great potential in ninjutsu, which Naruto nurtures.
Obviously, Haku and Naruto are the main characters. Haku, with his ice - based jutsu and complex backstory, and Naruto, the aspiring Hokage with his Nine - Tailed Fox power. They are the central focus as the story revolves around Haku adopting Naruto.
It could be about Hera, a character (presumably from a particular universe), who decides to adopt Naruto when he was little. Maybe it explores how Hera's different nature and abilities impact Naruto's growth and development in a fan - created scenario.