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.
If it's a more spiritual fanfiction, the mask could have a connection to the spirit world. Naruto wearing the mask could open a portal to that world or allow him to communicate with the spirits of past ninjas. He could then seek advice from the great ninjas of the past through the power of the mask.
He might become more reserved. Kakashi is often a bit aloof and mysterious, and wearing the face mask like him could make Naruto act in a more subdued way, not showing his emotions as openly as he usually does.
Perhaps in this fanfiction, there's a specific mission or situation. Maybe they are on a stealth mission together, and Naruto decides to wear a face mask like Kakashi to blend in better or to follow some kind of ninja code that Kakashi has taught him for this particular task.
It could also be a form of self - protection. Wearing a mask might shield her emotions. Sakura has been through a lot, and like Kakashi, who may use the mask to hide his past traumas, she might be doing the same. For example, if she's trying to distance herself from her old self or past relationships that have caused her pain.
One possible reason could be for disguise. Maybe he is on a secret mission and doesn't want to be recognized easily. In the Naruto world, there are many dangerous foes, and wearing a face mask can help him blend in or hide his identity from those who might be targeting him.
Maybe it was Jiraiya. Jiraiya was a very important figure in Naruto's life. He could have given Naruto the mask as part of a training exercise. He might have thought that wearing a mask would force Naruto to rely more on his intelligence rather than his brute strength in certain situations.
The mask could make her look more like a lone wolf, similar to how Kakashi often gives off that vibe. Others might assume she has some hidden motives or a new, more secretive side to her. It might also attract different kinds of attention. Some might be intrigued by the new look and try to figure out why she's wearing it, while others might be a bit put off by the change as it goes against the more open and friendly image they had of her before.
Well, obviously, the addition of the face mask gives him a more mysterious look. His usually open and friendly face is partly hidden, which might make others view him with more caution or curiosity.
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.