One common trope is the 'outsider' trope. The cat girl is often an outsider in the Naruto world, which creates interesting dynamics as she tries to fit in. For example, in many stories, she has to learn the ways of the shinobi.
The 'protector' trope is also popular. Naruto often takes on the role of protecting the cat girl, or vice versa. It adds an element of heroism and emotional connection between the characters. In some fanfics, the cat girl may have a special ability that Naruto needs to protect so it doesn't fall into the wrong hands.