One possible reason could be a sign of extreme loyalty and friendship. Naruto might see Yang in a dire situation where she needs his arm for some crucial purpose, like to complete a powerful jutsu or to defend against an overwhelming enemy. He is known for his selfless nature, so sacrificing his arm would be in line with his character.
Another possibility is that Naruto and Yang have a special bond. This bond could be formed through shared experiences, like they both went through a difficult training together or survived a life - threatening situation. Because of this special connection, Naruto feels indebted to Yang or simply values Yang's life more than his own arm.
She might become more cautious. Having received Naruto's arm, she realizes the great sacrifice he made. This could make her think twice before engaging in battles recklessly, as she now has a part of someone she respects and doesn't want to waste this 'gift'.
Maybe he was protecting someone in Wave. He's always the self - sacrificing type, so he could have put himself in harm's way to save a villager or a friend.
It could add a lot of drama. The sacrifice of a limb is a huge deal, and it would change Naruto's abilities and his role in the story. It might make him more of an underdog, which could lead to new character development as he has to adapt to his new physical state.
Maybe he starts to train with one - armed techniques. He could learn from other one - armed ninjas if there are any in the fanfiction world. His friends would also play a big role. They might encourage him to keep going or help him in his training.
Maybe Naruto has discovered something about Sakura that goes against his values. His arm could be a physical manifestation of his strength and determination to confront her about it. For example, if Sakura was involved in something unethical in the fanfiction, Naruto's confrontation through his arm could be a way to set things straight.
Perhaps he meets an ancient sage or a hermit who has the knowledge of regeneration. This character could guide Shino and provide him with the necessary herbs, incantations or mental exercises to regrow his arm. It could be a spiritual journey for Shino as he has to prove himself worthy to receive this knowledge.
In some fanfictions, Shino might regenerate his arm through special ninja techniques. For example, he could use a rare form of medical ninjutsu that he discovers or is taught. Maybe there's a hidden scroll in his clan's archives that reveals a way to regrow limbs.
Sasuke could be a candidate. Given their complex relationship, Sasuke might find a way to give Naruto a new arm as a way to atone for their past differences. He could have discovered some rare medical ninjutsu during his travels or come across a powerful artifact that he uses to create a new arm for Naruto.