Naruto would likely become more independent. Without his parents' attention, he would have to fend for himself more. He might grow up quicker and be more self - reliant. For example, he would have to learn to cook and clean for himself at a much younger age.
One possible reason could be that his parents are extremely busy with their own important ninja duties. In the Naruto universe, ninjas often have to go on dangerous missions. His parents might be so preoccupied with protecting the village from external threats that they simply don't have the time to notice Naruto. Another reason could be some sort of curse or spell that has made them oblivious to Naruto's existence. This could be part of an evil plot by an enemy who wants to isolate Naruto and make him feel alone.
It could be that in a special mission, Naruto discovers a hidden jutsu that allows him to communicate with the spirits of his deceased parents, leading to a touching reunion.
Perhaps Naruto has always felt different from others in the village. And when he finally learns about his parents, he realizes that their actions, even if they were for a good cause like protecting the village, still made his life very difficult. He might be angry that they didn't find a better way to handle things so that he didn't have to suffer so much growing up.
His relationship with his parents would be loving. Minato would be a strict but fair father, teaching Naruto about ninjutsu and the responsibilities of being a shinobi. Kushina would be the warm, affectionate mother, always there to comfort and encourage Naruto. They would support his dreams and be proud of his every achievement.
It might make him more distant from his friends at first. He could be so consumed by his anger towards his parents that he withdraws from his usual social circle. For example, he might avoid spending time with Sasuke or Sakura because he is too preoccupied with his feelings about his parents.
A plot for this type of fanfic could revolve around Naruto's inner turmoil. He could be constantly haunted by the question of why his parents neglected him. This could lead him to make some bad decisions, like getting involved with the wrong people. However, through a series of events, he starts to realize that he can create his own family and support system. He then begins to build a new life for himself, one that is not defined by his parents' neglect but by his own strength and the relationships he chooses to cultivate.
In this kind of situation, Naruto might first feel extremely sad and lonely. He could start by trying to prove himself to others. Maybe he'd focus on his ninja training more than ever, using it as a way to distract himself from the pain of being forgotten by his parents.
The village would be in chaos. Naruto was seen as the hope for the future, so his death would leave a huge void. His friends like Sasuke and Sakura would be devastated. They might turn against Naruto's parents, leading to more conflict in the village. Also, the balance of power in the ninja world could shift as Konoha would be weakened without Naruto.