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.
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 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.
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.
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.
This act of hiding his skills might also make Hinata feel special in a way. Naruto could be choosing to only show his true self to her gradually, which would give her a sense of being unique in his eyes. This could lead to a deeper emotional connection between them, as she would feel like she is the only one he trusts enough to eventually reveal his full capabilities to.
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.
It could also be part of a strategic move. By hiding his bloodline, he can surprise his opponents in battle. They would underestimate him based on not knowing about his true powers, and then he could turn the tables on them when the time is right. This gives him an edge in combat situations.
He might use some special jutsu or seals. For example, he could use a sealing technique to suppress the signs of his bloodline. This way, others wouldn't be able to detect it through normal means like sensing chakra.