Well, in the context of fanfiction, it's often about taking the existing characters from a known story and creating new scenarios. 'hermione is claimed by moony fanfiction' might be a statement about a specific fan - created story. Moony could be a character created by the fanfiction author or an existing character from the source material. The 'claim' part could be related to a relationship dynamic, like a romantic or a more complex relationship where Moony has a hold on Hermione in the story's world - view.
In fanfiction, 'claimed' can have various interpretations. 'Moony' might be a character (could be a werewolf reference perhaps, like Remus Lupin's nickname in the 'Harry Potter' series). So, it might imply that in this fanfiction, Moony has a special connection or right over Hermione, like he has declared her as his in some way, be it through a magical bond or a strong emotional attachment within the fictional narrative.