His personality might also include a sense of honor. Even though he is arrogant, he could have a code of conduct. For example, he would not use underhanded tactics in a fight. If he makes a promise, he would keep it. This aspect of his personality would add depth to his character in the fanfiction and create interesting interactions with other characters who may or may not share his sense of honor.
He would likely be portrayed as arrogant. Given his status as a powerful and ancient figure in his original lore, in DxD fanfiction he would probably look down on most of the characters. He would act as if he is above the petty squabbles of the DxD world.
His personality would be a mix of pride and a sense of superiority. He'd walk around the school as if he owns the place. However, he might also have a sense of honor. For example, if he made a promise to a character in the DxD world, he would keep it, but in his own haughty way. He might also be somewhat dismissive of the school's rules, believing that he is above them.
Gilgamesh can be portrayed as a powerful and haughty figure. He could walk around the world of Danmachi with an air of superiority, looking down on the 'lesser' adventurers. His flamboyant style and his love for grandeur can be emphasized, like always wearing the most elaborate and expensive armor.
In some fanfictions, Gilgamesh's powers are magnified to an extreme. He can control not just the Gate of Babylon but also manipulate time and space more freely. For example, he can create time - loops to his advantage in battles.
First, do your research on each of the source materials. Know the power levels, the personalities of the characters in Naruto, Gilgamesh's lore, and the world - building of DxD. Then, come up with a unique concept that can blend these three elements together. For example, you could have a crossover where a Naruto character is transported to the DxD world and meets Gilgamesh there.
His confidence would skyrocket. Gilgamesh is extremely self - assured, and Naruto, if influenced by him, would become even more so. He'd be more outspoken about his own abilities and less likely to doubt himself in tough situations.
He might become more confident, bordering on over - confident like Gilgamesh. Naruto is already confident, but with Gilgamesh as his father, he could have an even greater sense of self - importance.
One great Naruto, Gilgamesh and DxD fanfiction is 'The Convergence'. It has an interesting plot where the main character from Naruto somehow gets involved in the world of DxD and encounters Gilgamesh. The story is well - written with great character interactions.
Their relationship could be portrayed as a mentor - mentee one. Gilgamesh, with his vast knowledge and power, could guide Sailor Moon in becoming a more powerful fighter. He could teach her about the ancient ways of combat and magic that he knows. Sailor Moon, in turn, could show Gilgamesh the power of modern - day values like hope and love.
He could be integrated as a powerful enemy at first. He might target the academies because he sees them as places that are trying to control and limit power, which goes against his own philosophy. However, as the story progresses, he could have a change of heart after seeing the selfless acts of the RWBY characters. He could then use his powers to help them against a common enemy like Salem.
In Marvel fanfiction, Gilgamesh is often more of a superhero - like figure compared to his original mythological self. He may have enhanced physical abilities and be more directly involved in modern - day battles. For example, his strength might be on par with the Hulk in some stories.