Well, they might be really embarrassed at first. Naruto could turn bright red and stutter, while Hinata might faint from the shock. Then they would probably avoid each other for a while, until their friends notice the strange behavior and try to get them to talk it out.
Well, it could be that they have a sleepover at Hinata's place. They might cook a simple meal together like ramen. And then, while sitting around, Naruto could accidentally fall asleep first. Hinata might then take a moment to watch him sleep peacefully, blushing a bit as she realizes how much she cares for him. Later, she might cover him with a blanket and quietly go to sleep herself.
They might visit the local market. Naruto would be excited about all the different foods and items, and Hinata would be happy to follow him around. They could buy some cute souvenirs or some new ninja tools for Naruto. Then they could sit at a small cafe and enjoy some tea while talking about their friends and family.
In a Naruto and Hinata date fanfiction, they could start their day by visiting the memorial stone. Naruto would tell Hinata about his friends who sacrificed themselves. Then they would take a walk in the forest, holding hands and enjoying the peaceful nature around them. Hinata might shyly give Naruto a flower she picked along the way.
There could be a scenario where Kushina comes back to life somehow in the fanfiction. She might then play matchmaker between Naruto and Hinata, using her knowledge of Naruto to help Hinata understand him better. For example, she could share stories of Naruto's childhood that would make Hinata feel closer to him.
It could also result in a change in the way the village views their relationship. Since Naruto is a hero, his saving of Hinata would be a big deal. This could lead to the village elders or the people in general being more accepting of a possible romantic relationship between them. For example, they might start to see Hinata as a more important figure in Naruto's life and give her more respect.
Well, in a 'naruto absorbs hinata fanfiction', Naruto could absorb Hinata's gentle and kind-hearted nature along with her skills. This might change his personality a bit, making him more empathetic. And perhaps he could use Hinata's family techniques in a new and creative way, like combining the Gentle Fist with his Rasengan.
Perhaps in the fanfiction, there's a tournament or a competition. Naruto would be eager to prove himself, Hinata would be quietly determined, and Renamon could show off her combat skills. Their interactions during the event could lead to new friendships and rivalries. They might also learn new techniques from each other during the process.
One possible story could be a post - war scenario. Naruto has finally returned to the village as a hero. Hinata, who has always loved him secretly, gathers the courage to confess her feelings. Naruto, realizing how much Hinata means to him, leans in for a kiss. It could be a moment full of emotion, with the villagers looking on happily, seeing the two of them together after all they've been through.
One possible plot could be that Naruto and Hinata are on a mission together. During the mission, they face a difficult obstacle that they can only overcome by relying on each other completely. After they succeed, the adrenaline and the new - found trust lead to a spontaneous first kiss.
Another possibility is a complete character distortion in the fanfiction. The writer might decide to create a 'bad Naruto' version where he has lost all his positive traits. However, this is quite far - fetched considering the strong foundation of Naruto's character in the original series. It would be a very different and probably controversial take on the Naruto - Hinata relationship.