It could be due to a battle injury. Maybe he got into a really tough fight with a powerful enemy, and in the process, lost an eye. For instance, a fight against a rogue Akatsuki member who has a very dangerous eye - related jutsu.
This change in Naruto having one eye could lead to a whole new character arc. Maybe he'd be more self - conscious about his appearance, which could affect his relationships. He might also develop new jutsu that are more suitable for his one - eyed state, like a jutsu that uses his remaining eye's chakra in a more focused way.
It might be due to some sort of bloodline fusion. Naruto is known for his Uzumaki heritage, but perhaps there was an unexpected encounter with another clan's power that merged with his own, and as a result, one of his eyes turned red as a new and unique ability emerged.
One possibility could be through a forbidden jutsu experiment gone wrong. Maybe some rogue ninja was trying to create a super - powered being and Naruto ended up being the subject. The Sharingan was transplanted into him, but only one eye was successful.
In some fanfictions, he might obtain it through a powerful jutsu gone wrong that somehow fuses Uchiha DNA with his own. Maybe during a battle where he's exposed to some strange chakra energy related to the Sharingan.
Well, in some fanfictions, he might obtain it through a strange encounter. Maybe he stumbles upon an ancient relic during a mission that contains the power of the broken eye dojutsu and it somehow bonds with him.
It might have the ability to see through illusions that normal eyes can't. Since it's a dojutsu, even if it's broken, it could still have some enhanced visual powers. For example, it could detect the tiniest movements of an enemy, giving Naruto an edge in combat.
The third eye might have the power of long - distance vision. Naruto could use it to spy on enemy camps or look for missing comrades from afar. This would be a useful addition to his skills, especially when planning strategies or rescuing hostages. He could also use it to keep an eye on the Akatsuki's movements across different regions without having to be physically close.
He might gain enhanced perception abilities, which would be a huge boost to his combat skills. With the Sharingan, he could predict his opponents' moves more accurately.
In terms of his romantic relationships, if there were any potential love interests, they might be more hesitant. However, Naruto's determination and positive attitude could still win them over. His relationships with his teammates from Team 7 would likely shift. They would need to adjust their battle strategies to account for his one - eyed state. His bond with Hinata could also be tested as she might worry more about his safety and his ability to protect himself and the village.