In this kind of fanfiction, Kakashi could be portrayed as someone who is learning to balance his ninja life with his married life. He would be very supportive of the OC's dreams and goals. He would also be a bit more open about his emotions, not as closed - off as he was before getting married.
Kakashi would likely be shown as a loving and protective husband. He would still be the skilled ninja we know, but he would also have a soft side for his OC spouse. He might share his past traumas with her and let her in on his more vulnerable side.
Kakashi would become more nurturing. In the original, he was a teacher, but as an adoptive father, he'd have to be more affectionate. He might show his face more often to Naruto, as a sign of trust, and be more open about his emotions.
In such fanfiction, the Kakashi OC often has unique physical features. For example, they might have distinct hair color or eye shape that sets them apart.
The story might be about the OC having a special power. Kakashi is initially intrigued by this power and then falls for the person behind it. Once married, they work together to use the OC's power for the good of the village. They might also have some domestic scenes, like cooking together and having small arguments over silly things that show their normal married life.
Kakashi might be initially surprised. But then, he would probably use it as a teaching moment for Naruto. He could say something like 'Naruto, stealing is not the way of a ninja.' And then give him a punishment like extra training.
In many fanfictions, Kakashi is depicted as the reliable and intelligent ninja. He is the one who comes up with plans and strategies. Anko is seen as a strong - willed woman. She is not afraid to speak her mind and her loyalty to the village is often a key part of her character. For example, in some stories, she might be the first to jump into a fight to protect the village, while Kakashi assesses the situation from the sidelines before joining in.
It could be an original character created just for the fanfiction. Maybe a mysterious ninja woman who crossed paths with Kakashi during a mission and they had a brief but intense relationship.
Well, Naruto might be more reserved in Kakashi's generation. He would be among older and more experienced ninjas. He would have to prove himself more quickly. He might not have as much room for his wild and carefree antics as he did in his own generation. He'd be learning from different mentors too, which could shape his jutsu usage and battle strategies in a new way.
Their daily life would probably be filled with quiet moments. Kakashi, being a private person, would enjoy simple things like having tea with Hanare in the morning. Hanare, on the other hand, might be more outgoing and try to get Kakashi to socialize more with their friends in the village. They would also train together, with Kakashi teaching Hanare some of his signature jutsu.
Sakura would likely become more assertive in the relationship. She's used to being independent and now has to deal with sharing her life with Kakashi. For Kakashi, he might become more open. He has always been a bit of an enigma, but with Sakura in his life, he would have to let her in. He might start to show more of his emotions, especially when it comes to protecting their new - found relationship.
Kakashi would likely be very concerned. He would immediately assess Naruto's injuries. If they were serious, he would use his medical skills to start treating him right away. His first reaction would be to make sure Naruto was stable and out of immediate danger.