One common theme is identity. Percy has to figure out who he is now as a hellhound, different from his normal self. Another theme could be acceptance, as he has to deal with how others perceive him in this new form.
One common theme is the struggle with identity. Bella has to come to terms with being a Hellhound instead of a normal human or a vampire - in - waiting. Another theme could be power and its consequences. Since Hellhounds are often associated with great power, she might have to deal with how that power affects her relationships and the world around her.
In a fanfiction, the hellhound could be a protector of Percy instead of an enemy. It could be that the hellhound was once a pet of a powerful god who turned evil, and Percy helps it break free from the evil influence. So the hellhound then becomes loyal to Percy and helps him in his quests, like warning him of approaching monsters or even fighting alongside him against stronger foes.
A major theme is secrecy. In the 'Harry Potter' universe, being an Animagus without registering is illegal. So, in these fanfictions, the characters who are hellhound Animagus have to keep their identity a secret. This secrecy often leads to a lot of tension and plot twists. For example, they might be suspected of being dark wizards just because they are hiding their Animagus form. Also, friendship is a theme. Sometimes the hellhound Animagus characters form unique bonds with other characters who either help them hide or discover their true form.
Perhaps the hellhound is a part of a prophecy. In the fanfiction, it could be foretold that a hellhound will either bring great destruction or be the savior of the demigod world. Percy then has to figure out which path the hellhound is on and try to influence it to the side of good if it's the one that could cause destruction.
There's also a fanfic where a hellhound becomes a protector of Percy's sister. In this 'Percy Jackson Hellhound Fanfiction', the hellhound's loyalty and the way it interacts with the characters in the Percy Jackson universe are really interesting. It shows a different side of these usually menacing beasts.
Fanfiction.net is a great place to start. There are tons of 'Percy Jackson Hellhound Fanfiction' there. You can search by tags like 'hellhound' and 'Percy Jackson' to narrow down the results.
One popular 'Percy is a hellhound' fanfiction might be 'Percy's Hellhound Adventure' where Percy discovers his new form as a hellhound and has to navigate a world that now fears him. It has some really interesting plot twists.
Transformation is often a theme. The hellhound monster girl might change or the person she's in love with might transform in some way, either physically or emotionally, because of their relationship. For example, the human might become more accepting of the monstrous world or the hellhound girl might become more 'human - like' in her emotions. Also, there's the theme of adventure. They usually have to go through a lot of challenges and adventures to be together, like fighting against other monsters who oppose their relationship or facing the judgment of their respective communities.
One common theme is friendship. Despite the harem aspect, the relationships often start as friendships. Another theme is adventure. Just like in the original Percy Jackson series, the fanfictions usually involve quests and battles.
Another theme is loyalty. The loyalty between Percy and Blackjack is unwavering, and fanfictions like to highlight this. For example, there are stories where Blackjack stays by Percy's side even in the most dangerous of situations, and Percy in turn does everything he can to protect Blackjack.