Naruto might become more serious about combat. Ryu Hayabusa is known for his intense focus in battle, and Naruto could adopt this trait. Instead of his sometimes impulsive fighting style, he would be more calculated, thinking several steps ahead like Ryu.
His physical abilities would likely improve in different ways. Ryu is extremely agile and has great strength. Naruto, influenced by Ryu, could start to focus more on his own physical conditioning. He might develop a new set of taijutsu moves that are more similar to Ryu's sword - based attacks, which would make him a more well - rounded fighter in close - quarters combat.
Naruto's view of honor and loyalty could also change. Ryu Hayabusa has a strong sense of honor in his battles. Naruto, seeing this, might start to reevaluate his own reasons for fighting. He could become more concerned with fighting for the right reasons and upholding a certain code, rather than just for the sake of protecting his friends and village. This would add a new layer to his character, making him more complex and perhaps more respected by his enemies as well as his allies.