In this fanfiction, Naruto might name the puppy after one of his friends. Maybe he takes the puppy on his ninja missions and the puppy ends up being really helpful, like sniffing out traps or finding hidden enemies. It could also be that the puppy has some special abilities, like being able to communicate with Naruto telepathically.
A Border Collie might also be a possibility. These dogs are extremely intelligent. Stiles would have a great time teaching it all kinds of tricks. The Border Collie could also help Stiles in some way, like herding or using its intelligence to solve problems that Stiles might face. It would be a very active and engaging puppy for him.
His daily routine would be quite different. Instead of just focusing on ninja training and missions, he now has to make time for the puppy. He might start training the puppy to be a sort of 'ninja - dog' too. This would add a new aspect to his life and he would have to balance his duties as a ninja and a pet owner. And his friends might start coming over more often just to play with the puppy, which would bring more social interactions to Naruto's life.
The fanfiction could be about the adventures Stiles and the puppy have. They could go on hikes together in the forest near his town. During these hikes, they might encounter strange things or other supernatural beings. The puppy could either be scared or curiously investigate. Stiles would have to protect the puppy and also figure out how to deal with whatever they come across.
He might meet Hinata. She is kind - hearted and would surely be interested in the puppy. She could offer to help Naruto take care of it, like making a little bed for the puppy.
Perhaps in the fanfiction, Nico gets the puppy as a gift from a mysterious figure. The puppy is a special breed that is only known in the demigod world. Nico has to learn how to take care of this unique puppy. He has to figure out what it eats, how to train it, and also how to protect it from the various dangers that lurk in his world.
Sasuke could also be a main character in some Naruto puppy fanfiction. He might have an interesting relationship with the puppy. For example, at first he might be dismissive of the puppy, but as the story progresses, he realizes the puppy's importance. Another possible main character could be Sakura. She could be the one who helps Naruto take care of the puppy, especially if it gets injured or sick.
Another possibility is a monster that is attracted to the puppy's pure and innocent energy. This monster sees the puppy as a source of food or just something to torment. Nico has to fight off this monster to protect his new furry friend.
In the fanfiction, Naruto might take the puppy back to the village. He could name it something cute like 'Kiba Jr.' and train it to be a helpful ninja dog.
One interesting Naruto puppy fanfiction could be about Naruto finding a magical puppy that has special powers. For example, the puppy might be able to sense danger before it arrives and warns Naruto, which helps him in his missions.