He might become more independent. Without the protection of his parents, he has to fend for himself. So he could learn survival skills faster and become stronger in combat.
After being banished, Naruto could become more reclusive initially. He might isolate himself to avoid getting hurt again. However, he would still have his strong will deep inside. As he faces various challenges on his own, he gradually builds up his confidence in a different way. He no longer relies on the approval of his parents or the village. Instead, he focuses on his own self - worth. He might also develop a new perspective on friendship, realizing that true friends will accept him no matter what. And this could lead him to form deeper and more meaningful relationships in the future.
Naruto may grow bitter at first. After all, being banished by his own parents is a huge blow. But as time goes on, he could realize that he needs to prove himself. He might start traveling around, meeting different people and learning new ninja techniques. This experience could make him more understanding of different cultures and values, and he may become more empathetic and less impulsive. He could also start to question the village's values that led to his banishment, and in the process, develop his own set of beliefs.