Generally, in the realm of fanfiction, Moony is not depicted as harming Hermione during his transformation. It's a common trope to maintain their positive relationship.
Most fanfictions don't have Moony hurting Hermione when he turns. This is because fans often prefer to keep the characters' connections intact and free from such conflicts.
One key plot point could be that Moony has a history of protecting those he considers friends or allies. In the wizarding world lore, he has shown loyalty and kindness despite his lycanthropy. So in this fanfiction, it might be that he has previously saved Hermione from some danger, which makes her certain he won't hurt her.
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.
To find out who the author is, you could try searching for the fanfiction on popular fanfiction websites. Look for any author names or pen - names associated with it. Sometimes, these websites have a 'by' section next to the title which will tell you who wrote it.
Moony might be protective of Hermione because he has a strong sense of justice. In the wizarding world, Hermione is a Muggle - born, and she often faces discrimination. Moony, being a member of the Order of the Phoenix, is against all forms of prejudice. He would naturally want to protect her from any harm, whether it's from Death Eaters or just general bigotry within the wizarding community. Also, Hermione's intelligence and her role in fighting against the dark forces make her an important asset, and Moony would understand the need to safeguard such a valuable ally.
One common theme is the exploration of an unexpected friendship. Since they are from different generations in the wizarding world, seeing how they bridge that gap is often explored. For example, Hermione's modern - thinking and Moony's more traditional ways.
Moony might start to avoid Tonks while getting closer to Hermione. He could form a study group or some sort of alliance with Hermione, leaving Tonks out. This would create a rift between Tonks and Moony, and a bond between Moony and Hermione.
He might immediately go into a protective mode. He could use his potions knowledge to quickly make a healing draught for her. After all, Snape is very skilled in potions, and Hermione being hurt would likely trigger his instinct to help.
Often, the relationship develops through shared experiences. They could be facing a common threat, like a new dark magic that's emerging. Working together to combat this, they rely on each other's skills. Hermione uses her quick thinking and vast knowledge of spells, while Moony uses his experience and werewolf - related insights. This cooperation makes their bond stronger and more complex.
In some fanfictions, during battles at Hogwarts, Moony is often shown as standing in front of Hermione to shield her from dark spells. For example, when Death Eaters attack the school, he might push her out of the way of a Killing Curse. Another instance could be when Hermione is being bullied by some Slytherins for being a Muggle - born. Moony steps in and scares them away with his werewolf - like presence. He also might accompany Hermione when she has to go to some dangerous places, like the Forbidden Forest at night, to protect her from any lurking creatures or dark wizards.
There's a fanfiction called 'Hermione and Moony: A Forbidden Friendship'. It delves deep into the relationship between them in a world where their friendship is not easily accepted. It shows how they support each other through various challenges in the wizarding world. It's quite engaging as it also brings in other familiar characters from the Harry Potter series to add more depth to the story.