Kakashi's training would likely improve Naruto's chakra control, which would change his fighting style significantly. With better chakra control, Naruto could perform his jutsus more quickly and with less waste of chakra. He might be able to use continuous, smaller - scale Rasengans rather than always relying on the big, power - hungry ones. Also, his taijutsu could become more refined as he can now channel chakra more effectively into his punches and kicks, adding more power and precision to his close - range attacks.
The training could lead Naruto to be more versatile in combat. Kakashi, being a master of many jutsus, might expose Naruto to different types of techniques. This could result in Naruto incorporating elements of stealth or ranged attacks into his fighting style. He could learn to use shadow clones not just for distraction but also for coordinated attacks from different angles. This would make him less predictable in a fight and a more well - rounded ninja.
Kakashi's training might make Naruto more strategic. For example, instead of just relying on brute force with his Rasengan, he could start using it in combination with feints and misdirections. If Kakashi teaches him how to read an opponent's movements better, Naruto can time his attacks more precisely.