One idea could be that Naruto gains new powers. For example, if his DNA was changed to have some Uchiha traits, he might be able to use Sharingan - like abilities. This could completely change the way he fights and strategizes in battles.
Naruto's view of himself and his purpose in life could also change. He might start to question his identity as the Jinchuuriki of the Nine - Tails. With new DNA - based powers, he could feel like he has a different role to play in the ninja world. He might explore new ways to use his powers for the greater good, which would be a significant development in his character.
One possible consequence is new and unexpected abilities. For instance, if his DNA is changed to incorporate some sort of spirit energy, he could gain the ability to communicate with the dead. Another consequence could be changes in his appearance, like his hair color or eye color changing. This can also lead to social isolation as his friends might not recognize him at first.
Perhaps he would change to Naruto Storm. 'Storm' can represent his powerful and sometimes tempestuous nature. In the series, Naruto has shown great strength and determination that could be likened to a storm, which is both destructive and at the same time a force of change.
His character would become more secretive. Instead of being the open - hearted Naruto we know, he'd have to keep things to himself. For instance, he couldn't share all his thoughts and experiences with his friends right away.
His confidence could turn into over - confidence bordering on arrogance. As a villain, he might think he is above everyone else and that his way is the only right way. He would no longer listen to advice or consider the consequences of his actions on others, believing that he can handle any situation on his own, no matter how dangerous or unethical.
Clothing changes can also represent his emotional state. If he's wearing something more somber and dark, it might indicate a period of self - reflection or dealing with a difficult situation. For example, after a major battle where he loses a friend, he could change into all - black clothes as a sign of mourning.
Maybe it's from a powerful villain. In some fanfictions, this could be a really interesting twist. The DNA of a villain like Orochimaru could give Naruto some of his snake - like abilities or his knowledge of forbidden jutsu. However, Naruto would then have to struggle with the darker instincts that might come with that DNA. Another possibility is that it could be from an ancient and powerful demon. This would bring out a whole new set of challenges and powers for Naruto to deal with.
It could also be due to a prophecy or some sort of spiritual guidance. In the Naruto universe, there are often prophecies that guide the characters' actions. A prophecy might suggest that changing his name would bring about some great change or power. For instance, if there was a prophecy that a new name would help him unlock a hidden power or unite different ninja clans under a new banner.
In some Naruto fanfictions, Naruto might absorb DNA through special jutsu or abilities. For example, he could have a unique kekkei genkai that allows him to take in and assimilate the genetic material of others. This could potentially give him new powers or abilities related to the DNA he absorbs, like if he absorbs the DNA of a Sharingan user, he might gain some form of Sharingan - like abilities.