Well, he might gain some incredible powers. For example, he could have the power of Zeus to control lightning. He could use it in battles, making him even more formidable. Also, he might inherit the wisdom of Athena, which could help him make better decisions in tough situations.
Naruto's character could develop in terms of his leadership skills. As a Greek god, he'd likely have to lead or be part of the godly community. His natural leadership from being a ninja could be enhanced. He'd also have to learn to control his emotions better, as Greek gods often have tempers, and Naruto would need to find a balance between his old self and his new godly self.
Apollo could be a likely candidate. Apollo is the god of music, prophecy, and healing. Naruto's strong sense of justice and his ability to inspire others could be seen as traits inherited from Apollo. Also, Naruto has a certain charm that could be related to Apollo's association with the arts. And if Naruto had some healing abilities from Apollo on top of his own ninja skills, it would make him even more of a valuable asset in battles.
Well, he might gain incredible powers like the Greek gods. He could control the elements, for example, just like Zeus controls lightning. Maybe he'd also have a new look, with a more god - like appearance. And his relationships would change too. His friends might view him differently, with a mix of awe and perhaps a bit of fear.
In this fanfiction, Naruto could gain the powers of a God of Destruction through a special encounter. Maybe he meets an ancient being who sees his potential. His training to control these powers would be intense. He would have to learn to balance his old ninja values with the new role of maintaining balance in the universe through destruction when necessary.
One possible plot could be Naruto being the son of a Greek god in secret. He discovers his divine heritage during a mission in the Naruto world. With his newfound godly powers, he can control elements in a way no one else can, like summoning lightning bolts similar to Zeus or controlling water like Poseidon. This would completely change the power dynamics in the Naruto universe.
In a Naruto - Greek god fanfiction, Naruto could be a new - born god. Since he has that never - give - up attitude, he could be seen as the god of perseverance. He would likely have to face the politics and power struggles among the Greek gods. His friends in the Naruto world could be transformed into minor deities or demigods, and they'd all embark on epic adventures together in the realm of Greek mythology.
It's also likely that Naruto becomes a god dragon slayer as a result of a prophecy. The fanfiction could explore how he initially struggles with this new role. He has to deal with the expectations that come with being a 'god' - level dragon slayer. Along the way, he might make new allies, like other dragon slayers or magical creatures who recognize his potential and help him in his journey to master this new power.
One possible ally could be Poseidon. Naruto's connection to water - based jutsus might make Poseidon interested in him. They could form an alliance where Naruto helps Poseidon in battles using his water techniques in a new and unexpected way, and Poseidon, in return, helps Naruto understand the politics and power dynamics of the Greek god world. Another ally could be the nymphs. These nature spirits might see Naruto as a protector of sorts. Since Naruto has always had a soft spot for nature in his own world, he could bond with the nymphs and they could help him navigate the forests and hidden places of the Greek world, as well as provide him with information about other gods and mortals.
I think Hinata would also be an ally. She has always been in love with Naruto and would support him no matter what. And the rest of the Konoha 11 would probably be his allies too. They have all fought together and have a sense of camaraderie. With Naruto as a god - like figure, they could help him spread his message of peace and use his powers to protect the village and the world at large. They would be the ones who understand Naruto the best and would be there to assist him in any way they can.