Well, Goku's training is intense. It might involve extreme physical conditioning like his gravity training. Naruto could be pushed to his limits in terms of strength and speed. He'd probably learn about ki control, which is different from chakra but could enhance his abilities. Goku might also teach Naruto about the importance of a strong mental state during battle, something Naruto already has a bit of but could be refined.
If Naruto were trained by Goku Black in fanfiction, it would be a wild combination. Goku Black is from a different universe with different power systems. He could introduce Naruto to concepts like ki, which might blend with Naruto's chakra in interesting ways. Naruto's physical abilities would likely skyrocket, and his combat strategies would be completely revolutionized. He might start using more acrobatic and flashy moves, like Goku Black does.
Naruto might become more calm and collected. Goku has a certain simplicity and focus in his personality. Naruto could pick up on that and not be as impulsive as he usually is.
His speed would increase. Goku Black is very fast, and his training could make Naruto move at blistering speeds. Also, Naruto's power attacks would be stronger. Goku Black's training methods would push Naruto to new limits.
Well, perhaps it could be about Izuku learning Goku Black's unique combat styles and techniques. Maybe Goku Black would push Izuku to his limits in training, helping him gain new powers and a more ruthless edge in battle.
Another possibility is that in the world where Goku Black comes from, there is an enemy who follows Goku Black to Izuku's world. This enemy could be a powerful Saiyan or a being with a dark ki similar to Goku Black. They might see Izuku as a weakness in Goku Black's plan and try to eliminate him first, making them the main antagonist in the fanfiction.
In a Goku Naruto crossover, both characters have their own strengths. Goku's physical strength and energy attacks are off the charts. His ability to instantly teleport and sense ki gives him an advantage in combat. Naruto, though, has a unique power system. His connection to the Nine - Tails and his ability to use different types of chakra make him a force to be reckoned with. If we consider a battle, Goku's power might seem greater on the surface. But Naruto has the advantage of being able to surprise his opponents with his ninjutsu and clones. Also, Naruto has a strong willpower that has allowed him to overcome many tough situations, which could play a role in a fight against Goku.
Well, Naruto would probably gain some really unique magical abilities. Fairy Tail mages are known for their diverse magic, and Naruto could combine his chakra skills with something like Fire Magic or Celestial Magic. He might become even more powerful in combat, with new ways to attack and defend.
Naruto would gain better combat awareness. Kurama's experience in battles can be passed on to Naruto. He'll be able to read his opponents better, know when to attack and when to defend. This will make him a more formidable opponent in combat situations.