Well, it depends on the specific fanfiction. Sometimes, Naruto absorbing Kami could result in him having a deeper connection to the spiritual world. This might allow him to communicate with spirits more easily and gain insights into things that were previously hidden from him. He could also use this new connection to access more powerful forms of sage mode, if the fanfic writer decides to go in that direction.
Maybe it's a completely new and unknown kami. A kami created specifically for this fanfiction. This kami could have unique powers and a different view of the ninja world compared to the existing characters in Naruto. It would add a fresh and exciting element to the story.
Maybe it's an existing character from Naruto who has been elevated to Kami status. For example, Tsunade could be turned into a Kami, and Naruto's relationship with her could be a very different dynamic from their previous ninja - leader relationship. Or it could be Kaguya, who was already a very powerful being, and in this fanfiction, she reforms and becomes a Kami and Naruto's wife.
In fanfiction, the 'kami' could be an original deity created by the author. This new 'kami' could have its own motives and reasons for giving a gift to Naruto. Maybe it's a kami that has been observing Naruto's journey and decides to interfere to help him achieve a greater purpose. It could be a kami associated with nature, like a kami of the wind or the fire, and the gift could be related to that element.
Maybe Jiraiya. Since Jiraiya was Naruto's mentor and taught him a lot of things. He might have some knowledge about summoning kami and pass it on to Naruto.
Perhaps it could be a female version of an existing kami from Naruto lore. For instance, a female counterpart of the Sage of Six Paths. She would have vast knowledge and power, and her training of Naruto would be a way to pass on that ancient wisdom and strength.
Many 'kami naruto fanfiction' pieces tend to blend the spiritual elements of Kami with Naruto's more physical and combat - oriented world. They might explore how Kami's existence affects the balance of power in the ninja villages. Also, these fanfictions sometimes create new relationships between Kami and other characters in the Naruto universe, like Kami having a special bond with Kakashi or Sasuke in some stories.
Yes, it could be considered a relatively new concept as the amount and variety of fanfiction has exploded in recent years, and the idea of Naruto 'absorbing' these diverse fan - created ideas is something that has emerged as a result of the growing and evolving fan culture.
In some fanfictions, when Naruto absorbs the bijuu, he might gain overwhelming power. This could lead to him being able to easily defeat powerful enemies that were previously a threat. For example, he could single - handedly take on the Akatsuki without much difficulty.