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.
The male protagonist transmigrated to the world of Naruto and became Kakashi, starting an unusual ninja journey. In the process, he encountered all kinds of interesting characters, including other ninjas, teammates, and enemies. He experienced many difficulties and challenges, but in the end, he grew and succeeded, becoming a powerful ninja.
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.
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.
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.
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.
In some yaoi fanfiction, Naruto can be depicted as a prodigy like Kakashi. Writers often play with the characters' traits and exaggerate them for the sake of the story. Naruto already has his own natural talent in the original series, and in fanfiction, this can be amplified to be on a par with Kakashi's prodigious abilities.
Another possibility is that Naruto wears the mask as a tribute to Kakashi after a significant event. It could be that Kakashi sacrifices himself to save Naruto and the village. So, Naruto dons the mask to carry on Kakashi's legacy and to always remember the lessons he learned from him.
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.