Maybe he wants to blend in better. If he's in a situation where he needs to gather information undercover, showing off his skills would blow his cover. So he hides them to seem like an ordinary person until the right moment to strike.
Well, it shows his humility. By hiding his skills, he's not seeking the spotlight, which is a sign of a humble character. This can attract other characters to him and make them trust him more easily.
Perhaps he has hidden the full extent of his Sage Mode abilities. He might be able to stay in Sage Mode for a much longer time than he has shown so far, or have some other undisclosed powers within that mode, like the ability to sense enemies from much greater distances.
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.
Maybe he wants to protect his loved ones. If his enemies know his true strength, they might target his friends and family to get to him. So, by hiding his skills, he can keep them out of harm's way while still being able to fight when necessary.
Perhaps Naruto is waiting for the right moment to reveal his skills for maximum impact. He could be planning a big surprise for his enemies or wants to make a grand entrance at a crucial time. For example, in a major battle against a powerful foe, he could suddenly unleash all his hidden skills and turn the tide of the battle, which would be more effective than showing them off gradually.
Well, he might use simple distractions. For example, he could create a minor commotion to draw attention away when he's about to use a particular skill subtly. Maybe he pretends to be clumsy or make a small mistake on purpose so that others don't suspect he has advanced skills.
In many fanfictions, Tony Stark hides his PTSD for various reasons. One reason could be his pride. He's seen as a strong, self - reliant hero, and admitting to PTSD might seem like a weakness to him. Also, he might not want to worry his fellow Avengers, especially those he feels responsible for protecting, like Peter Parker.
First, decide on the reason why Peter is hiding his identity. Is it to protect his loved ones? Or is it because his identity being known would put him in danger? Then, create a world around him that makes this secrecy necessary. For example, if he's in a world full of supervillains, it makes sense for him to hide. Also, think about the little details, like how he acts differently when he's in his 'hidden' identity compared to his true self.
In a Peter hides his identity fanfiction, he might use advanced technology to conceal who he really is. For instance, he could have a holographic device that changes his appearance completely. This allows him to move freely among his enemies without being recognized. The story could explore the moral dilemmas he faces while keeping this big secret from his loved ones.