Naruto might become more calm. Minato was a very composed person, and if Naruto becomes like him, he'll lose some of his impulsive nature. For example, instead of rushing into battle head - first all the time, he'll start to think more strategically like Minato did.
Naruto may also become more reserved in his emotions. Minato didn't show his emotions as openly as Naruto usually does. So, Naruto might keep his feelings more in check, especially in front of enemies or during important diplomatic meetings, in order to project a more stable and reliable image, just like his father.
His confidence could turn into over - confidence bordering on arrogance. As a villain, he might think he is above everyone else and that his way is the only right way. He would no longer listen to advice or consider the consequences of his actions on others, believing that he can handle any situation on his own, no matter how dangerous or unethical.
Naruto could pass on his determination. He's always been someone who doesn't give up easily, and Minato might inherit that. Also, his loyalty. Naruto is extremely loyal to his friends and the village, and Minato could grow up with those values. Maybe even Naruto's love for ramen would be passed on in some comical way.
If Naruto becomes like Kenpachi, his personality would become more rough and wild. He would be more direct in combat and less likely to hold back. He might also lose some of his optimistic charm in the process, becoming more of a battle - hungry brute.
Naruto might become more withdrawn like Gaara was initially. Gaara was isolated due to his power and the fear others had of him. So Naruto could start to keep to himself more, losing some of his boisterous and friendly nature.
One of the main similarities is their self - sacrifice. Minato sacrificed himself to save the village and his son. Naruto has also shown that he is willing to put himself in harm's way for the greater good. He's always the first to jump into a dangerous situation if it means protecting those he loves. Another aspect is their leadership qualities. Minato was a great leader as Hokage, and Naruto has developed into a great leader as well, inspiring those around him.
Well, it could start with Naruto being in a situation where he feels lost about his own path. Then, he starts researching about Minato more deeply. He finds out about Minato's early struggles, how he overcame them, and his great contributions to Konoha. As Naruto delves into Minato's story, he realizes that Minato was a true hero in every sense. This realization makes Naruto look up to Minato, and he decides to incorporate Minato's values into his own ninja way.
One characteristic is their similar determination. Minato was determined to protect the village at all costs, and Naruto has the same unwavering resolve. This determination drives them to keep pushing their limits and achieving great things.
It could be that Naruto is trying to prove himself. He wants to show that he can be as great a fighter as his father. Also, he might have received some training or knowledge transfer from someone who knew Minato well. This could have inspired him to adopt Minato's fighting style. He may also be in a situation where his normal fighting style isn't working, so he turns to Minato's as a last resort.
He would probably be more power - hungry. Thanos was constantly seeking power through the Infinity Stones. Naruto, who has always been about protecting his village and friends, could shift his focus more towards personal power gain. This might lead him to isolate himself from his friends as he pursues greater power, just like how Thanos was mostly alone in his quest.
One common ability is their speed. Minato was known as the Yellow Flash for his incredible speed. Naruto, with his Sage Mode and later forms, can also move extremely fast. Another is their use of the Rasengan. Minato created the Rasengan, and Naruto has mastered it and even developed it further.