It could also be that he had a plan to disrupt the traditional way of the Chunin Exam. Naruto is known for his unorthodox thinking. He might have raised his hand to introduce a new style of combat or strategy that he had been thinking about. He wanted to show that there are different ways to approach the challenges in the exam and not just follow the old rules.
Maybe he saw an opportunity to help his friends. If there was a task or a challenge in the Chunin Exam that required someone to step forward, Naruto, being the selfless person he is, raised his hand to protect or assist his comrades. For example, if there was a dangerous opponent that his friends were having trouble with, he would volunteer without hesitation.
Perhaps Naruto raises his hand to answer a really tough question in the written part of the Chunin Exam. He could use some of his unique experiences or the wisdom he's gained from his friends to come up with an unexpected but brilliant answer. This would surprise the examiners and his fellow candidates, and might earn him some respect from those who used to look down on him.
Perhaps he showed an enhanced sensory ability. In the Chunin Exam, being able to sense opponents better can be a great advantage. Naruto might have raised his hand to volunteer for a task that required this ability, and it was a sign that he had improved his sensing skills to a new level. He could detect even the faintest chakra signatures and movements of his opponents, which would have surprised everyone.
Maybe he realizes the exam is too dangerous or he discovers some unfairness in it. In the original Naruto story, Naruto has faced many difficulties and moral dilemmas during the Chunin Exam. So in the fanfiction, similar situations might push him to quit.
Naruto may become more confident. By raising his hand, he's taking initiative, which is a sign of growing self - assurance. He's no longer waiting for others to pick him or tell him what to do.
Naruto would likely become more self - reliant. As a ronin, he doesn't have the support of a village. So during the Chunin Exam, he has to trust his own instincts and skills more. He may also become more cautious as he realizes he can't always count on backup.
He might face disappointment from his friends and mentors. His friends who were also participating in the exam might feel let down, and his mentors, like Kakashi, could be concerned about his decision and how it will affect his future as a ninja.
One possible scenario in such a fanfic could be Naruto easily overpowering his opponents during the Chunin Exam. For example, in the written test, he might use some new, godlike power to read the minds of the examiners or sense the correct answers. During the combat rounds, he could defeat his foes with a single move, leaving everyone in awe. His newfound power might be related to some ancient ninja art he discovered or a special training he underwent secretly.
One possible reason could be that Naruto faced an extremely tough opponent in the exam. Maybe the opponent had some special jutsu or skills that Naruto couldn't counter at that time. Another reason might be that Naruto made a critical mistake during the exam, like being overconfident and underestimating his enemy.
Maybe in a fanfic, Naruto is dealing with a personal crisis or a family matter that makes him unable to attend the Chunin Exam. Or perhaps there's a magical curse that keeps him away from it.
One possible fanfic could be about Naruto and Temari teaming up during the Chunin Exam in unexpected ways. Maybe Naruto helps Temari when she's in a tough situation against an opponent she underestimated. They could form an alliance that surprises everyone.