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.
The player might change the title and his name associated with the novel so that it becomes difficult to trace back to him. He could also use some legal means like copyright restrictions to limit its availability if possible.
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 has some dark secrets in his past that he doesn't want to be known. For example, he might have been involved in something illegal or unethical that could damage his reputation in the world of the web novel.
It can create suspense. Readers will be curious about what he is hiding and keep reading to find out. For example, it might be revealed gradually through flashbacks or other characters' investigations, which adds an element of mystery to the story.
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.
One possible reason could be that his eyes hold a special power that he doesn't want others to discover easily. For example, it might be a new type of Sharingan or a unique ability related to his Uzumaki heritage that he needs to keep secret to protect himself or those around him.
Maybe he wants to surprise his opponents in battles. He could be waiting for the perfect moment to reveal his full power and turn the tables on his enemies.