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.
Perhaps he just acts in a way that doesn't draw attention to his bloodline powers. He doesn't show off any abilities that are obviously related to his bloodline and instead focuses on more common ninja skills in public.
Another possibility is that he uses some sort of disguise or misdirection. He could create false chakra signatures or pretend to be a normal ninja without any special bloodline. This would involve a lot of skill in controlling his own chakra and fooling 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.
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.
One possible reason could be that he doesn't want others to pity him. Naruto has always been a proud and strong - willed character. His scars might be a reminder of painful past experiences, and he prefers to deal with them privately rather than showing vulnerability to others.
Well, with the Omnitrix bloodline, Naruto might gain the ability to transform into various alien forms. This could enhance his physical strength, speed, and even give him new jutsu - like an alien form might have unique energy blasts. His combat style would become more diverse, and he could surprise his opponents in new ways.
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.
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, Naruto might hide his pain by putting on a big smile. He's always been the type to try and be positive in the face of his friends. He could also distract others with his goofy antics, like making a joke or doing something silly to shift the focus away from his inner turmoil.
He might use simple language on purpose. For example, he could pretend to be confused about things he actually understands well. He may also make silly mistakes intentionally to give the impression that he's not as smart as he really is.
Since Naruto has a strong connection with the Nine - Tails, he could create a bloodline ability that lets him tap into the Nine - Tails' power in a more controlled and unique way. Instead of just using the Nine - Tails' chakra for strength and speed boosts, he could use it to create a sort of chakra - based armor that not only protects him but also amplifies his own jutsu when he channels his chakra through it.