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.
His friends might react with shock and confusion. They might not understand why he has been hiding this from them, and it could cause a rift in their relationships until he explains the reasons behind it. For example, some friends might feel betrayed that he didn't trust them enough to share this secret.
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.
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.
Naruto might end up feeling extremely lonely. His family has always been an important part of his life. Without their support and presence, he could become depressed or start making even more reckless decisions. Also, if his family tries to search for him, they could get into danger themselves in the process, which would be an unintended consequence of his hiding.