In some fanfictions, Naruto might get the scar on his eye during a particularly intense battle with a powerful enemy. Maybe it was a close encounter with a rogue ninja's weapon that managed to leave a mark on his eye area.
Hermione might be the one. With her extensive research skills and vast knowledge of magic, she could have stumbled upon a way to remove the scar. She was always determined to help Harry, and this would be just another of her great contributions.
His scar might make some people more intimidated by him. They could see it as a sign of his dangerous experiences and be a bit afraid to get too close. For example, new acquaintances in the fanfic might be hesitant to approach him at first.
Maybe Ash doesn't want Serena to worry about him. He might think that the battle scar is a sign of his vulnerability and he wants to always appear strong in front of Serena.
Zoro often puts himself between Luffy and danger. For example, when facing strong opponents, he'll be the first to step forward and engage, making sure Luffy is safe behind him.