Obviously, Naruto himself would be a key character as the story focuses on his serious training. Kakashi could also be important. He might be Naruto's guide in this new training regime, sharing his own experiences and wisdom to help Naruto grow stronger.
In the 'naruto trained seriously fanfiction', Naruto could be training with his friends in a more serious way. They might form a special training group where they push each other to their limits. For example, they could be training to improve their teamwork and combination jutsus. Naruto might focus on his speed and strength training while also learning how to better coordinate with his friends' abilities, like Sasuke's Sharingan - based attacks and Sakura's medical and combat skills.
One possible plot could be Naruto making great leaps in his ninja skills. He might learn powerful jutsu more quickly under Jiraiya's intense training regime. For example, he could master new forms of Rasengan faster and also gain better control over his chakra.
It could be a rogue ninja from a forgotten clan. This ninja might have a vendetta against Naruto's village and has powers that are difficult to counter. So, Naruto has to train to kill him to protect everyone.
Another option could be Itachi. Although Itachi is from a different village and has his own complex situation, in a fanfiction scenario, he could secretly train Naruto. Itachi has extremely powerful jutsus and a deep understanding of the Sharingan. Training under him would give Naruto a very different perspective on power and combat, not to mention some insights into the Uchiha clan.
Naruto would likely become more disciplined. Jiraiya's strict training would force Naruto to focus and follow a routine, which is different from his usual impulsive self.
A likely main summon could be Gamabunta. He's big, powerful, and has a long - standing relationship with Naruto. He could teach Naruto some really advanced water - based jutsu.
It could be a powerful dark wizard who wants to control the dragons and sees Naruto as a threat because of his newfound dragon - trained powers.
It could be an unknown ninja from a far - off village who specializes in Storm Release. This ninja might have heard of Naruto's potential and decided to train him.
It could be an old, retired ninja who lives on the outskirts of the village. This person has seen the hardships Naruto faces and decides to take him under their wing.
Obviously, Naruto and Asuma would be the main characters. Naruto, the protagonist of the Naruto series, is the one being trained. And Asuma, a respected jonin in the Hidden Leaf Village, is the trainer.