Hinata would likely become more independent. For example, if she was often relying on Naruto for emotional support, she'd have to find that within herself. She might become more assertive in the village, using her skills to protect it as Naruto did.
He would be filled with rage. Naruto has a strong sense of justice and the fact that someone took Hinata away from him would fuel his anger. He would vow to find and punish whoever was responsible. He might even become reckless in his pursuit of vengeance, endangering himself and those around him. His friends would have to step in to try and bring him back to his senses.
It could make Naruto more introspective. He might question his own worthiness of Hinata's sacrifice. This could lead to him delving deeper into his own beliefs and values. He may also become more empathetic towards others who have lost loved ones, as he now has first - hand experience of that kind of pain. He would grow in maturity, realizing that his actions have consequences not just for himself but for those around him who care about him deeply.
One common theme could be sacrifice. Hinata might die to save Naruto or the village. Another theme could be grief, as Naruto and their friends would have to deal with her loss. And there might be a theme of revenge, where Naruto or others seek to avenge her death.
He would be filled with a deep sense of grief. Naruto has always cared about Hinata, and her death would be like a part of him has been ripped away. He might isolate himself for a while, blaming himself for not being able to protect her. But eventually, he would use his pain as motivation to get stronger and fight against whatever caused her death.
One possible storyline could be in a dark AU (Alternate Universe). Maybe there's a powerful new enemy that targets Hinata specifically because of her connection to Naruto. This enemy could have some sort of vendetta against the Hyuga clan and sees Hinata as the key to their downfall. Naruto is then left to deal with the grief and also find a way to avenge her death, which could lead to a whole new arc of him exploring darker powers or making some difficult moral choices.
Well, in this fanfiction, an ending might be that Hinata, in her grief, leaves the village for a while to find herself. When she returns, she has become stronger and more confident. She then devotes her life to making the village a better place, just as Naruto would have wanted. Another ending could be that the whole village unites even more tightly after Naruto's death, with Hinata at the forefront of this unity, as she was the last person Naruto protected.
A common scenario in such fanfictions is that Hinata sacrifices herself in a war - torn situation. For instance, in a great ninja war, Naruto is the key to victory but is targeted by the enemy's most powerful forces. Hinata, with her unwavering love for Naruto, jumps in front of a massive attack aimed at Naruto, knowing full well that it will cost her life. This selfless act then serves as a major turning point in the story, inspiring Naruto and his comrades to fight even harder.
He would feel a deep sense of guilt, thinking that if he had been stronger or more aware, he could have saved her. Naruto might also start to cherish the memories he had with Hinata more, and this could change his personality a bit, making him more somber at times. He would probably vow to protect the things that Hinata held dear, like her family and the village.