He might become more cautious. Tsunade is a more calculating ninja compared to some of Naruto's previous mentors. So Naruto could start to think before he leaps, rather than just charging into battle head - first all the time.
Naruto could develop a greater sense of responsibility towards the village. Since Tsunade is very much about protecting Konoha, her influence could make Naruto see the bigger picture of his role in safeguarding the village. He might also become more patient. Tsunade's training methods may require a lot of repetition and precision, which would force Naruto to slow down and be more patient in his learning process.
Naruto might become more calculating. Urahara is a very strategic person, and under his training, Naruto could start thinking more before acting. For example, instead of just rushing into a fight, he'd analyze the situation first.
Naruto might become more sly. Since Loki is a trickster, Naruto could pick up some of his devious ways. He may not be as straightforward as he used to be.
His personality might become more brooding. With Darth Vader's influence, Naruto could lose some of his naivete and become more cautious.
His personality might change in several ways. He would probably be more humble as he realizes the vastness of the power he is being exposed to. Also, he could become more of a mentor - like figure to the younger ninjas in Konoha. Since he is getting trained by such a powerful entity, he would have a greater sense of responsibility and would want to pass on his knowledge. He might also become more open - minded, as the Grand Priest's teachings could expose him to new ways of thinking and different cultures if the fanfiction has elements of different universes interacting.
Naruto would likely become more disciplined. Tsunade is strict, so Naruto would have to follow her rules. For example, he might learn to control his impulsiveness better. He'd also become more well - rounded as Tsunade could teach him things other than just his regular ninjutsu. Maybe he'd be more patient too.
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 personality might be more reserved. Tsunade is not as boisterous as some of Naruto's other mentors. So he could be less likely to jump into things without thinking. For instance, he might analyze a situation more carefully before acting.
His confidence could take on a different form. While Naruto has always been confident in his abilities, training with Zoro would make him more self - assured in a more reserved way. Zoro's tough training would force Naruto to prove himself not just to others but also to himself, and this could lead to a more mature kind of confidence. Also, Naruto might become more introverted as he focuses more on his training, similar to how Zoro is often focused on his own improvement.
His relationship with Sasuke might be affected. Naruto might approach Sasuke differently, with new strategies learned from Zetsu. He could be more secretive about his intentions towards Sasuke, which might either make Sasuke more curious or more distrustful. With his friends in Konoha, they might be a bit wary of Naruto at first because of his new training source. But once they see that Naruto is still on their side, they would support him.
His combat abilities would become more diverse. Madara could teach him new forms of taijutsu and ninjutsu. For example, Naruto might learn some of Madara's signature space - time ninjutsu, which would give him an edge in battles. His chakra control would also improve as Madara is very proficient in chakra manipulation.