In some fanfictions, Harry might change his identity to protect his friends. For example, if Voldemort was specifically targeting those close to Harry, he could change his look and name so that his friends would no longer be in danger. He could also change his identity to study dark magic secretly in order to better understand Voldemort's power and find a way to defeat him without putting others at risk.
Hermione is often involved. She might be the one helping Harry with the spells or potions to change his identity, like brewing the Polyjuice Potion correctly. Ron could also be involved, perhaps providing moral support or getting into trouble while trying to keep Harry's new identity a secret.
One consequence could be that his relationships change. His friends might not recognize the new 'soul - changed' Harry at first, leading to some initial confusion and distance in their friendships.
In some fanfiction concepts, he might change his soul through powerful magic spells. Maybe he discovers an ancient spell in a hidden book in the Room of Requirement that has the power to transform his very essence, his soul.
He could use magic items like the invisibility cloak all the time. In fanfiction, the cloak might be enhanced to not only make him invisible but also mask his magical signature, so no one can detect his presence through spells.
If Harry Potter changes his name to Wizard in fanfiction, it might symbolize a new beginning or a desire to break away from his past. It could also make for some really interesting plot twists. For example, his friends might not know it's him at first, and there could be a whole mystery around who this 'Wizard' really is. This could add an element of intrigue to the fanfiction.
With his friends, it could initially cause confusion. They are so used to calling him Harry that the new name might be a bit of a shock. But if they understand his reasons, they would likely support him. For example, Hermione might be the first to adapt and help others adjust, using her logical thinking to see the benefits of the name change.
One good small change could be in the character development. For example, Neville could start showing his courage a bit earlier in the fanfiction. This would add an interesting twist as it would make the story deviate slightly from the original in a positive way. It could also change the dynamics within the group of friends at Hogwarts.
Sasuke might be initially suspicious. Given their complex relationship, Sasuke would likely want to know the real reason behind Naruto's identity change. But once he understands the motives, he might respect Naruto's decision if it's for a good cause.
In some fanfiction, Harry changes his life by changing his attitude towards his enemies. Instead of always being on the defensive, he tries to understand them. For instance, he might reach out to some of the children of Death Eaters and tries to show them a different path. This not only changes his relationship with his former foes but also earns him respect from both sides of the conflict. It also changes the way the wizarding world perceives him, from a simple hero to a peacemaker.