Another fictional hawk could be 'Hawkeye' which is a name that can be associated with a hawk - like character. It gives the impression of a character with sharp vision and a focused, predatory nature, much like a real hawk.
One common theme is probably the 'opposites attract' scenario. For example, a very bubbly and outgoing character falling for the more reserved Suga. Another theme could be 'finding love in unexpected places', like on a tour or during a random encounter.
The Hawks' back story could involve their origin as a sports team. They might have started in a particular city with a group of passionate players and investors. Maybe they were initially part of a smaller league and then grew to be in a major one. Their name could be inspired by the characteristics associated with hawks, like speed and precision.
There are fanfics where the 'lov capture deku' scenario leads to an exploration of Deku's character growth. For example, while captured, he might start to understand the motives of the LOV members on a deeper level, which in turn changes his approach to heroism in the story. This can add a lot of depth to his character.
One aspect to consider in Hawks x Dabi fanfiction is the dynamic between their personalities. Hawks is often seen as more of a hero with a sense of duty, while Dabi has a darker, more rebellious nature. In many fanfictions, their interactions can range from intense rivalries to unexpected alliances. For example, some stories might explore how Hawks, with his loyalty to the hero system, might initially view Dabi as a pure villain. But as the story progresses, they could discover common ground or shared experiences that bring them closer together.