Maybe Naruto hides his genius to avoid unwanted attention. He might be afraid of being targeted by enemies or those who would use his abilities for bad. For example, in the original series, he already had a lot of people after him because of the Nine - Tails. By hiding his genius, he could be trying to keep a low profile and train in secret to become even stronger without interference.
It could be someone who is jealous of Naruto's hidden genius. Maybe a fellow ninja who senses that Naruto is hiding something and wants to expose him out of envy. This person might try to undermine Naruto at every turn.
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.
Sasuke could be one of the people who help him. Despite their past differences, they have a deep bond. Sasuke has his own skills and knowledge that could be useful in Naruto's situation, like his Sharingan abilities which could help in detecting enemies while Naruto is hiding his face.
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.
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.
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.