It would likely make his relationship with Iruka even more important. Iruka was one of the first to show Naruto kindness, and with his parents' absence, he would cling to Iruka as a father figure even more. Naruto might also be more eager to prove himself to his peers. He would want to show that he doesn't need his parents and can be just as good or better than those with a normal family. This could lead to some over - competitiveness at times.
One possible reason could be that his newfound 'godlike' powers make his family feel estranged. They might not understand his sudden transformation and the magnitude of his power, which creates a sense of fear or discomfort, leading them to ignore him.
One possible plotline could be Naruto growing up feeling extremely lonely and trying to find ways to gain his parents' attention even though they're not around. He might start to excel in ninja training not just to prove himself to the village but also in the hope that his parents would be proud if they were there. Another could be Naruto having vivid dreams about his parents and then waking up to the harsh reality of their absence, which could fuel his determination to find out more about them and why they ignored him.
Naruto may become more self - reliant. Without the support of his parents, he has to figure things out on his own. He might grow up faster, learning to take care of himself at an early age. For example, he would have to learn how to cook, clean, and do other basic life tasks all by himself.
Maybe his parents are dealing with some internal conflicts or secrets. They could be involved in something dangerous or forbidden, and they think that by ignoring Naruto, they are keeping him safe from the consequences of their actions. It could also be that they are under some sort of spell or mind - control that makes them act as if they don't care about him.
Naruto might initially feel sad and confused. He could try to prove himself to his friends by working hard on his ninja skills. For example, he might train extra hours to show his friends that he is worthy of their attention.
One common plotline is Harry finding a surrogate family. It could be his friends like Ron and Hermione who become like his true family. They support him and give him the love and care he didn't get from his parents.
In this kind of fanfiction, Naruto may also feel a great deal of sadness and confusion at first. However, as time goes on, he could use that pain as motivation. He might think that if his family won't recognize him, he'll make a name for himself in the ninja world in a way that they can't ignore. He could start taking on dangerous missions, not just for the village but also to show his family what they're missing out on.
Emotionally, Naruto would have to deal with a whole new set of family relationships. He grew up without his parents, and now having them back would be a huge adjustment. He might struggle to fit into a 'normal' family dynamic, and there could be some friction as they all get to know each other again.