One possible reason could be for protection. Maybe there are threats out there targeting him, so by hiding his appearance, he can move around more freely without being recognized. For example, if there are rogue ninja who want to take revenge on him for past battles, hiding his face would make it difficult for them to track him down.
To gain an advantage. Just like in the original series where he often used surprise to his benefit. In fanfiction, hiding his power allows him to do the same. He can catch his opponents off - guard.
Naruto might hide his feelings because he doesn't want to burden others. He has been through a lot in his life, like being an orphan and facing discrimination in the village. He may think that sharing his negative feelings, such as loneliness or self - doubt, will make others worry about him. So, he chooses to keep them to himself and always show a positive, determined side to the people around him.
Maybe he is ashamed of it. Some past works might not be up to his current standards, or perhaps there are elements in the novel that he doesn't want to be associated with anymore.
Maybe he's trying to hide his identity for a secret mission. In some fanfictions, Naruto might be undercover, and covering his face is a simple way to avoid being recognized.
One possible reason could be that he is on a secret mission and doesn't want to be recognized. He might be infiltrating an enemy organization or spying on someone. Another reason could be that he has some new power or mark on his face that he wants to keep hidden until he fully understands or masters it.
The main character of the City of Rebirth concealed his identity because he was a cultivator, but he did not want to be recognized because he did not want to cause unnecessary trouble. In addition, he might also be afraid of exposing his cultivation ability because cultivators were often seen as aliens in society and were seen as threats with powerful abilities. Therefore, the protagonist would try his best to hide his true identity to avoid unnecessary attention.
Another reason could be related to his personal growth. He might be trying to master the power of the eye in private. Naruto has always been one to face challenges alone at first. By hiding his eye, he can focus on understanding and using its power without distractions or the pressure of others' expectations.