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.
The name 'Shadow - Hawk' could also be a name for a fictional hawk. It implies a hawk that is stealthy, perhaps hunting in the shadows or having a mysterious quality about it. These names help to create an image in the reader's or viewer's mind of what the hawk character is like in the fictional world.
One common theme is romance. Many fics explore a romantic relationship between the reader and Hawks. Another theme could be friendship, where the reader becomes a close friend to Hawks and helps him through his struggles.
One key element is the location where they were founded. It provided the context and the pool of potential players and fans. Another is the people behind the formation, like the founders and early coaches.