One common theme is self - discovery. When Naruto is alone, he often has time to think about who he is and what he wants. Another theme is inner strength. He has to rely on his own abilities and not depend on others. For example, in many fanfictions, he overcomes great difficulties alone using his own skills.
There are many reasons. Firstly, Naruto's character has a lot of potential for this kind of story. He has always had a sense of loneliness in the original series, being an outcast in the village. So, fanfiction writers like to explore this aspect further. Secondly, it creates a lot of drama. When Naruto is alone, he has to face challenges without his usual support system, which makes for an exciting read. Thirdly, it allows for different character developments. Alone, Naruto can grow in ways that might not be possible in the main story.
A really interesting 'Naruto is alone' fanfiction is 'Naruto: Alone Against the World'. It takes place in an alternate universe where Naruto is the only one left with his unique powers and everyone else has either turned against him or disappeared. He has to face powerful enemies all by himself. Then there's 'The Lonely Naruto' where Naruto is isolated because of a false accusation. He spends his days training alone in the forest, slowly growing stronger and more determined to prove his innocence. 'Alone in the Abyss' is also a good one. In this story, Naruto falls into a deep, dark place, both literally and metaphorically, and has to find his way out on his own.
Self - discovery is a common theme. When Naruto is alone, he has time to think about who he is and what he wants to become. Another theme is growth. He has to become stronger on his own without relying on his friends all the time.
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 meet an old enemy who has also changed after the war. This enemy might now be in a similar situation of being alone and they could form an unexpected bond as they understand each other's isolation.
He might meet an old sage who has been living in seclusion near the village. The sage could see Naruto's loneliness on his birthday and offer him some ancient ninja knowledge.
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.
Maybe an ancient evil ninja who was sealed away long ago but has now been released. This antagonist could have powers that nullify any communication or summoning jutsu, forcing Naruto to fight alone. He would be extremely powerful and know many forgotten and deadly jutsu.