Naruto would likely become more confident. Knowing he has the blood of a Greek god in him would give him an extra boost. He might also be more curious about the world outside of the ninja realm, since his Greek heritage would open up new possibilities. His sense of justice could become more intense, as Greek gods often have strong ideas about right and wrong.
Naruto's character would experience a significant transformation. He would no longer be just the underdog ninja trying to prove himself. With his Greek god heritage, he would have a new sense of purpose. He might become more of a leader, not just in Konoha but in the broader world. His values could shift to incorporate some of the Greek values associated with his divine father. For example, if his father was Apollo, he might value art and knowledge more. His appearance might also change slightly, having an otherworldly glow or some physical features that hint at his godly lineage. And his attitude towards his enemies would be more confident and fearless, knowing he has divine powers on his side.