A possible plotline could be that a new enemy targets Kakashi because of his distinct face features, believing there is some hidden power in his appearance. Naruto then has to protect Kakashi. Another plotline could be a magical spell that gets cast on Kakashi's face, changing his expressions uncontrollably, and Naruto tries to find a way to break the spell.
Well, for starters, Kakashi has to deal with Naruto's hyperactive and sometimes reckless behavior. Naruto often acts without thinking, which could put him in danger. Sasuke, with his complex emotions and the burden of his clan's massacre, is also a handful. Kakashi needs to make Sasuke understand that revenge is not the only way forward. Additionally, Kakashi has to ensure that both Naruto and Sasuke get along well with each other. There could be rivalry between them, and Kakashi has to manage that in a way that doesn't harm their relationship or their growth as ninjas.
In the fanfiction, Kakashi might face the challenge of Naruto's insecurities. Naruto has always had a complex about being alone and not having a family. Kakashi would have to find ways to make Naruto feel secure and loved. Also, dealing with Naruto's powerful and sometimes uncontrollable chakra could be a problem. Kakashi would need to train Naruto to master his chakra properly without it overwhelming him.
One interesting concept could be a story where Naruto has to draw Kakashi's face as part of a training exercise. He struggles to capture the mystery and calmness in Kakashi's eyes. Another could be a time - travel fanfic where Kakashi's face in his younger days is a key element in changing the future of the ninja world. For example, someone from the future sees Kakashi's face in an old photo and realizes a connection to a major event that needs to be altered.
One challenge could be Naruto's stubbornness. Naruto has his own ideas and ways of doing things, and getting him to listen and follow Kakashi's guidance might be tough. Another is dealing with Naruto's past traumas. Kakashi would need to help Naruto overcome his feelings of loneliness and being an outcast. Also, Kakashi has his own responsibilities and missions, so finding time to be a proper adoptive father could be a struggle.
Often, Gai is paired with Kakashi in Hurt Kakashi fanfiction. Gai, with his unwavering belief in friendship and his eternal rivalry with Kakashi, can be a great character to interact with a hurt Kakashi. He might try to pull Kakashi out of his slump through their friendly competition. Also, Rin is sometimes included. Since she has a significant past with Kakashi, her presence in the fanfiction can either be a source of comfort or more pain, depending on how the story is written.
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.
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.
Often, Naruto is paired with Kakashi in such fanfictions. Their bond from the original series can be explored in new ways in the context of Kakashi's reincarnation. For example, Naruto might be the one to discover Kakashi's reincarnated form and help him adjust.