His view of himself might become more complex. If he reads fanfictions where he is depicted as a super - powerful hero beyond what he already is, he could start to question his own limits. Or if he reads ones where he fails a lot, it might make him more self - critical.
Percy could gain a new understanding of the power of storytelling. Seeing how fans can take his world and create new and exciting tales might make him appreciate the stories of the Greek gods more. He might also start to see his own story as part of a larger tapestry that can be woven in countless ways by different people, which could give him a more inclusive and open - minded view of his own place in the world.
His view of power might change. In The Hunger Games, the Capitol holds extreme power over the districts, which is different from the power dynamics in Percy's world. He might start to think more about how power can be misused and how the oppressed can fight back.
It could also strengthen his bond with his friends. Realizing that others are interested in their story and are creating their own versions of their relationships could make Percy feel closer to his friends. He might even share some of the interesting fanfiction ideas with them and have a good laugh together.
His view of friendship could expand. In Naruto, friendship is very strong and characters are willing to sacrifice a great deal for their friends. Percy might see new ways to show loyalty to his own friends.
Their view could become more complex. If they see in the fanfiction how mortals imagine their powers and personalities, they might realize how much mortals are intrigued by them. Some gods might start to respect mortals more for their creativity in writing these stories. Others might become more disdainful, seeing how mortals sometimes distort their true natures in the fanfiction.
He might gain new perspectives. If the fanfiction shows him as more vulnerable than he thought, he could start to see himself in a different light.
They might see mortals as more creative. Since fanfiction often involves unique interpretations and new storylines, the gods would realize that mortals can come up with some very interesting ideas about them.
He might be intrigued. The fanfiction might show him a new side of the Greek mythological world that he's part of.
His view might expand. He'd realize there are countless other possibilities beyond what he knows in the ninja world. For instance, if there's a crossover with a futuristic world, he'd see how technology could be integrated into combat, which might make him think about new ways to use his own jutsu.
His view would be severely disrupted. President Snow has a very specific view of the Hunger Games as a means of suppressing the districts and maintaining his power. Fanfiction could present scenarios where the Games are not as effective in that regard. It could show the tributes having more agency or the Capitol being more corrupt than he wants people to believe. This would make him see the Hunger Games not as the powerful symbol of control he thought it was, but rather as something that can be easily subverted in the minds of the people, and he would do everything in his power to stop this new perception from spreading.