Naruto might cope by focusing on his goals. He's always been determined, so he could pour all his energy into achieving something in the modern world, like getting an education or mastering a new skill.
He could start writing in a journal. Since he has no one to talk to, he'd write down his thoughts and feelings. This would be a way for him to process his loneliness and also keep his memories of his old life alive. He might also try to find solace in nature, just like he used to do in the forests near Konoha.
In many such fanfics, it might show Naruto's early days in the village more harshly. Maybe it details how he was truly isolated, with no one to share his meals or his dreams. For example, it could describe his evenings alone in his small apartment, longing for a family or a friend to talk to.
He might focus on his training. By pouring his energy into getting stronger, he can distract himself from his lonely feelings. Naruto has always been determined, and training gives him a sense of purpose.
He could develop a sense of independence that is different from his usual teamwork - oriented self. In the face of being alone in modern Konoha, Naruto may start to rely more on his own judgment and skills. He might learn new jutsu or ways of thinking that he didn't have the chance to explore when he was always with others. This could also make him a more complex and nuanced character as he faces challenges on his own.
In many fanfictions, Naruto might start by training harder. He throws himself into his ninja training as a way to distract himself from the loneliness. It gives him a sense of purpose and also helps him become stronger.
Naruto may write letters to his friends who are away. He could pour his heart out in these letters, talking about how much he misses them and how he's doing. Writing can be a very therapeutic way to deal with loneliness. He might even include some little drawings like he used to do when he was a kid.
Naruto would likely be portrayed as a bit melancholy at first. He's used to being around his friends, and being alone on Christmas makes him feel a bit left out. But he still has his positive attitude deep down. He might be shown looking at the Christmas lights in the village with a sense of longing, yet also determination to make the best of the day.
Well, it might show Naruto in a modern setting, all alone, perhaps because he's the only one with his unique abilities. He could be constantly on the run from people who want to study or use him. And as he's alone, he'd have to learn to rely on himself in ways he never had to in the Naruto universe. He'd also likely have internal struggles as he misses his old friends and life.
She might be initially shocked and hurt. Sakura has always had Naruto as a constant in her life, so his sudden absence would be difficult to accept. She could become withdrawn and start to question her self - worth.
Naruto would probably be very excited at first. He'd be amazed by all the tall buildings and bright lights. But he'd also face some challenges. For example, he'd have to learn how to use modern technology like cell phones and public transportation. He might initially struggle with things like traffic rules. However, his adaptability as a ninja would help him. He'd quickly figure out how to blend in and make the most of the new opportunities in Tokyo, like trying different kinds of food.
Often, Naruto's loneliness in fanfiction is shown through his solitary moments. He might be sitting alone on the Hokage Rock, looking over the village that doesn't fully accept him. It's a visual way to represent his isolation.