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.
In a fanfiction where Naruto is trained by Goku Black, the first thing that might change is Naruto's approach to battle. Goku Black is known for his ruthlessness and determination. Naruto could learn from this and become more decisive in combat. His speed and strength would increase significantly. Goku Black might also teach Naruto how to better control his energy, allowing him to perform more powerful jutsus without tiring as quickly. Moreover, Naruto's perception of power levels and opponents would be altered. He'd start seeing the world of fighting from a different perspective, which could make him a more formidable ninja in the long run.