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.
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.
Another possibility is that Naruto has a plan that requires him to keep his skills hidden from everyone, including Hinata, for a while. He could be waiting for the right moment to reveal them and use them to surprise and save the day, especially when it comes to protecting Hinata from a big threat that he anticipates.
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.
He might want to protect himself. If others know how smart he is, he could become a target. Enemies might see him as a greater threat and go after him more aggressively.
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.
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.
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.
One possible reason could be fear of rejection. In the Naruto universe, he has so many expectations on him. If he reveals his true self which might be more vulnerable or different from the image people have of him, he could be shunned. For example, his experiences as a Jinchuriki made him an outcast initially, so he may be afraid to show more of his true self in case it causes more isolation.
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.