For a boy, they could go with Orion, a name associated with a great hunter in Greek mythology. It would symbolize strength and skill. And for a girl, they might name her Calypso, not just because it's a beautiful name, but also as a way to remember the different characters they've encountered on their adventures and the lessons learned from them.
I think their parenting style would be adventurous. Percy has always been into taking risks and exploring, and Annabeth is smart and strategic. They'd probably encourage their kids to be brave and use their wits, like taking them on quests that are suitable for their age, teaching them about the world of Greek mythology in a fun way.
Their relationship would likely become more nurturing. They would have to rely on each other more as they take on the role of parents. For example, when the child has a nightmare about monsters, Percy might be the one to comfort the child first while Annabeth figures out how to better protect the home. Then they would discuss their concerns and fears for the child together, strengthening their bond as they face these new challenges as a couple.
Well, Harry has the unique ability to see Thestrals because he has witnessed death. It's possible that one of their children could inherit this ability too, depending on how the fanfiction plays out. Hermione is very good at time - turning spells, though it's a dangerous magic. Their kids might inherit an inclination towards time - related magic, but hopefully in a more controlled and legal way. And of course, both Harry and Hermione are good at defensive magic, so their children would surely inherit strong defensive magical abilities.
One possibility is that there is a bit of a culture clash. Percy comes from a world where he's used to the demigod lifestyle and Annabeth has her own set of family values from her mortal family. So when they meet the parents, there could be misunderstandings. Maybe Percy doesn't understand some of the traditional mortal family things that Annabeth's parents expect, like formal dinners or certain etiquettes. And Annabeth might have to explain Percy's rather unorthodox upbringing to her parents, which could be quite an adventure in the fanfiction world.
In a family with two such powerful demigods, there could be a power struggle within the family itself. Their children might grow up feeling the pressure to live up to their parents' reputations. Moreover, Percy and Annabeth would have to decide how much of the demigod world they expose their kids to at a young age. If they expose too much too soon, it could be overwhelming for the children, but if they wait too long, the kids might be unprepared for the threats that come with being a demigod.
She might like the ones that focus on their romantic relationship. Since they have a strong connection in the original story, fanfictions that explore their love in different ways could be appealing to her.
Their relationship would change in many ways. During the pregnancy, Percy and Annabeth would have to communicate more effectively. There would be discussions about the baby's future, what kind of upbringing they want to give, and how to handle any potential threats. They would also have to support each other through the physical and emotional changes. Annabeth might have mood swings, and Percy would need to be there for her. And Percy might have his own insecurities about being a father, which Annabeth would have to help him through. All these things would transform their relationship into a more mature and interdependent one.
Percy might be a bit flustered and embarrassed. He's protective of his relationship with Annabeth, so having Magnus walk in might make him feel like their privacy has been invaded. He could quickly try to shield Annabeth or just look really shocked.
It could be that they adopt a group of children. Some of them are demigods and some are mortals who were all in a difficult situation. Percy and Annabeth's home becomes a haven for these kids. They teach them all about Greek mythology, train the demigod kids in combat and powers, and for the mortal kids, they teach them how to support their demigod siblings. This would create a really unique family dynamic full of love, adventure and learning.
One possible storyline could be their children going on a quest to discover a new hidden part of the demigod world. Maybe they have to find a lost artifact that is crucial for the safety of Camp Half - Blood. Another could be their children facing challenges at school, dealing with both normal school problems and the added pressure of being demigods.