He could become a more solitary and brooding character. In the ANBU, Naruto might use his pain as fuel for his missions. He could start to distance himself from his old friends, as the nature of ANBU work is often secretive and isolating.
He would likely become more withdrawn. Naruto is usually so open and exuberant, but heartbreak could make him close off. In ANBU, he might be quieter, more focused on the mission at hand. He'd still have his determination, but it would be a more solemn determination. His sense of humor might also disappear for a while as he copes with his pain.
In some fanfictions, Naruto might join Anbu because of Sakura to prove himself worthy of her. Maybe he thinks that by becoming an elite Anbu member, he can show her that he's strong and reliable.
Well, perhaps Naruto is heartbroken after losing someone dear, like Sasuke leaving again. He feels betrayed by the Hidden Leaf. In his despair, the Akatsuki approaches him, offering a sense of belonging and a new purpose. They might convince him that the Leaf is corrupt and that their goals, which could be about changing the ninja world in a more radical way, are worth joining.
Well, in such a fanfiction, perhaps Naruto has just lost Sasuke again and is deeply depressed. The ANBU, seeing his skills and his need for a distraction, recruit him. He starts off being a bit of a misfit in ANBU, not following all the rules because of his independent nature. But as he continues, he starts to understand the importance of their work. He might even form new bonds with his ANBU comrades, which slowly help him come out of his depression.
Well, Naruto might face a whole new set of challenges. In the ANBU, he could be pushed to his limits physically and mentally. Maybe he'd use his unique skills in stealthier ways compared to his normal fighting style. Also, his relationships with other ANBU members would be interesting to explore, as he's a bit of an outlier with his loud and brash personality.
In this kind of fanfiction, Naruto might face some really tough and secretive missions in ANBU. He could be trained in new and deadly ninja techniques. Maybe he would also form some unexpected alliances with other ANBU members, learning from their different skills and experiences.
In such a fanfiction, the plot could involve Naruto being constantly overlooked by the village. Fed up with this, he decides to join ANBU to prove his worth. He might face challenges like distrust from his ANBU comrades at first because of his reputation. But as he goes on missions, he shows his skills and determination, gradually earning their respect and changing their perception of him.
Well, in a fanfiction where Naruto joins ANBU, his training would intensify. He'd be trained by some of the toughest ANBU veterans. His skills in combat would become more refined as he'd learn to use weapons like kunai and shuriken with more precision. He may also develop new jutsu that are more suitable for covert operations. His growth as a ninja would be different from the regular path, focusing more on secrecy and assassination if required.
One possible plotline could be that Naruto, heartbroken from a failed relationship or the loss of a dear friend, throws himself into the dangerous and secretive world of ANBU to numb his pain. He might start off as a reckless agent, but gradually find purpose in protecting the village in a more covert way. This could lead to him making new, deeper friendships within the ANBU ranks.