Well, the dragon would obviously be a main character in its own right. It could have its own personality and motives.
There might be other characters from the original series who play important roles. For example, Daenerys might be in the fanfic. Since she was associated with dragons in the original story, she could have an interesting dynamic with Jon Snow now that he's also linked to a dragon. Maybe they compete for the dragon's loyalty or work together to use the dragon's power.
Then there could be some new characters created specifically for the fanfic. Maybe a dragon trainer who helps Jon Snow understand his new connection with the dragon. This character could introduce new plot twists and conflicts, like having different ideas about how to handle the dragon compared to Jon Snow.
Sansa Stark might be involved as well. Given her relationship with Jon Snow as his sister (though later revealed otherwise), she could play a role in protecting or being involved with the baby. Maybe she helps raise the baby in a world where Jon Snow is constantly facing threats.
Obviously, Jon Snow as a reborn dragon is the main character. But there could also be characters like Daenerys who might play an important role. She has her own connection with dragons, so her reaction to Jon's new form could be a significant part of the story.
Obviously, Jon Snow is a main character. He's usually depicted as having a special bond with the ice dragon. His character traits like his honor and leadership often play a big role in the story.
Tyrion Lannister could be involved. He was close to Daenerys and had a relationship with Jon as well. He might be the one to help protect the baby or offer his wisdom in raising the child. Another character could be Ser Davos. He was loyal to Jon and would surely be interested in safeguarding the future of Jon's heir.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
One common theme is power. The dragon gives Jon Snow a great deal of power, and these fics often explore how he wields it. Another theme is identity. Since Jon Snow has a complex identity, and the addition of a dragon connection further complicates it. There's also the theme of destiny. Fics may show that Jon Snow was always meant to have a connection with a dragon as part of his greater destiny in Westeros.
One popular 'Jon Snow Black Dragon' fanfic is 'The Bond of Ice and Dragon'. It tells a story where Jon Snow forms an unexpected connection with a black dragon. The story is filled with adventure and a touch of magic.
Brienne of Tarth is a character that can be paired with Jon Snow in fanfictions. Brienne is known for her loyalty and honor. She could serve as Jon's knight, protecting him and upholding justice in his kingdom. Also, Gilly could be part of the story. As Samwell Tarly's love interest and a person with knowledge from the far North, she could provide insights into the common people's needs and also help in matters related to the Night's Watch or the North in general.
Arya Stark might interact with him. She has her own set of skills and goals. Their reunion could be emotional, and they could work together to take revenge on those who wronged their family.
Daenerys Targaryen is often paired with Jon Snow in these fanfictions. Their connection in the original series, along with their both being strong leaders, makes for an interesting dynamic. They could rule Westeros together in a new era of peace and prosperity after Jon's rebirth.