Well, one similarity could be their determination. In the fanfic, like in the original series, both Naruto and Kakashi are very determined. Naruto is always striving to become Hokage and Kakashi has his own goals and missions he's dedicated to. They also might share similar combat styles in the fanfic, perhaps Naruto starts to adopt some of Kakashi's strategic thinking during battles.
Maybe Naruto admires Kakashi's skills. Kakashi is a highly respected ninja, and Naruto might want to be as good as him. So he starts acting like him to learn from him.
One similarity is their natural talent for combat. Both are likely to be very skilled in using various ninja techniques. Kakashi was known for his Sharingan and his ability to use a wide range of jutsus, and Naruto in this fanfiction would also have a natural aptitude for combat skills.
Naruto could show his 'like Kakashi' traits in his mentoring style in the fanfic. Kakashi is a great mentor to his students, and if Naruto is like him, he might start to take on apprentices and teach them in a patient and knowledgeable way, passing on not just ninja skills but also important life lessons.
Yes, in some fanfictions, Naruto can be like Kakashi. Writers might give Naruto some of Kakashi's traits, like his calmness in battle or his love for reading. This can make for an interesting twist in the story.
In the fanfic, Naruto could pick up Kakashi's habit of being a bit of a mystery. He might not reveal all his thoughts and plans right away. Also, his sense of humor could change to be more dry and understated, similar to Kakashi's. He may start using more one - liner type of remarks during interactions. Naruto might also show more patience in teaching and guiding others, as Kakashi is often seen doing with his students.
One example could be that Kakashi always makes time to train Naruto personally. He focuses on Naruto's unique strengths and weaknesses, just like a brother would do to help his sibling improve. Another example might be that Kakashi is there for Naruto during tough times, like when Naruto is feeling down about not being as strong as he wants. He gives Naruto words of encouragement and support.
It would be really strange. Naruto is much younger than Kakashi in the original story. But if it were a fanfiction, maybe it could involve some time - travel or alternate universe concept. Naruto could use his experiences to raise Kakashi in a different way than Sakumo did.
In this kind of fanfiction, Naruto might be dressing like Kakashi for various reasons. Maybe it's part of a mission where he has to go undercover. He could be trying to imitate Kakashi's cool and mysterious aura to deceive the enemy.
One common theme is mentorship. Since Kakashi is a great mentor in the original series, in these fanfictions, Naruto often tries to take on a similar role. He might mentor the younger generation, passing on the lessons he learned from Kakashi.