His physical abilities would be enhanced. Constantly running, climbing, and fighting in the forest would make him stronger and more agile. His stealth skills would be top - notch as he'd have to hide from the forest's predators.
Naruto could have a greater control over his chakra. Since Kushina would be there to guide him, he would likely avoid some of the pitfalls he faced in the original story. His physical strength might also be enhanced as Kushina could train him in ways that utilize his Uzumaki bloodline more effectively.
His chakra control would probably be better. In a temple, he might learn meditation techniques that help him master his chakra more effectively. Also, his physical abilities could be more refined in terms of balance and grace, like a monk's movements.
Naruto's combat style would be more refined. Sakumo was a highly skilled ninja, and he would teach Naruto better swordsmanship skills perhaps. Naruto's taijutsu could also be more precise and calculated. Also, Naruto might develop better chakra control earlier, as Sakumo could instill in him the importance of efficient chakra usage from a young age.
Naruto would be more in tune with nature. He would understand the rhythms of the forest, the behavior of animals, and the flow of natural energy better. This could potentially lead to him having an easier time mastering Sage Mode, if that is part of the fanfiction's storyline. His view of the world would be narrower in some ways, as he has only known the Forest of Death, but broader in others, as he has a deep understanding of the natural world that most ninjas lack.
In a fanfic where Naruto is raised in the Forest of Death, he might become extremely tough. He'd have to fight for survival from a young age. Maybe he'd befriend some of the dangerous animals there, learning their ways to stay alive. He could also develop unique ninja skills by adapting to the harsh environment of the forest.
His water - based abilities would likely be more refined. Amphitrite could teach him advanced techniques for controlling water, like creating complex water formations or using water for long - distance communication. He might also have a better understanding of the magic within the sea, being able to tap into hidden powers that normal demigods wouldn't know about.
Naruto's ability to control the Nine - Tails would be enhanced. Since the Sage has a deep understanding of the tailed beasts, he could teach Naruto how to fully harness the power of the Nine - Tails without the usual struggle. This would make Naruto not only stronger but also more in tune with the beast's power, allowing him to use it more effectively in combat. He could also potentially communicate with the Nine - Tails on a much deeper level, leading to new forms of cooperation between them.
His abilities might take on a more unpredictable edge. He could incorporate some of Joker's trickery into his combat. For example, using misdirection like Joker does in his schemes.
If Naruto was raised by Slenderman in fanfiction, his abilities would change drastically. His chakra control might be influenced by Slenderman's otherworldly energy. He could gain the ability to manipulate the environment in a more spooky way, like making the air feel cold and heavy around his opponents. Also, his Rasengan might take on a different form, perhaps with a dark, swirling energy around it.
His physical abilities would likely improve greatly. Whis could train Naruto to have better speed, strength, and agility, much like how he trains Goku and Vegeta in Dragon Ball. Naruto might also gain the ability to sense ki, which would give him an extra sense in battle.