One common theme is friendship. Since Rangiku has a lot of friends in the 'Bleach' universe, fanfictions often explore her deep bonds with them, like with Ichigo or Renji. For example, stories might show how she helps them through tough times.
I've also heard of a fanfiction that focuses on a more comical side of a Naruto - Rangiku Matsumoto encounter. For example, Naruto is confused by the strange new world he's in and Rangiku has to explain things to him in a very humorous way. Their different personalities, Naruto's naivete and Rangiku's laid - back yet strong - willed nature, make for a lot of comical situations.
A common trope is the 'fish out of water' scenario. Naruto being in the Bleach universe and trying to figure out how things work while Rangiku helps or hinders him. Another is the power - exchange trope where they teach each other their unique abilities. For example, Naruto shows Rangiku how to use shadow clones in a creative way, and she shows him how to use her sword's spiritual energy.
There's also 'Rangiku's Adventure Beyond the Seireitei'. This fanfiction takes her on an exciting journey outside the known areas, full of new challenges and character development. It really expands on her personality and abilities.
Another idea for the fanfiction could be a time - travel plot. What if Ichigo somehow travels back in time and meets a younger Rangiku? He could influence her growth and development, and in turn, she could have an impact on his view of the past. This would create a complex web of cause and effect, and it would be interesting to see how their actions in the past would shape the future of the Bleach world they know.
There may be some Rangiku Matsumoto fanfic on Archive of Our Own (AO3) as well. You can search for it by using relevant tags. Look for stories that explore her backstory, her loyalty to Gin, and how she copes with the various challenges in the Bleach storyline. Just be sure to avoid any content that might be inappropriate or against the site's terms.
Her past and how it has shaped her is also a frequent theme. Her time with Gin and how that relationship has influenced her actions and decisions in the present. Additionally, her place in the 10th Division of the Soul Society and how she interacts with the other members of the division. This can include everything from training sessions to just casual conversations around the division headquarters.
There's a fanfic called 'Silent Bonds'. In this one, the author delves deep into their past. It shows how Rangiku's presence has influenced Toshiro's growth as a Soul Reaper. The writing style is really engaging, and it gives a lot of insights into their personalities. You'll find their interactions very interesting, especially when they're training together.
A fanfiction could also explore how they deal with loss together. Both have experienced losses in their lives. They could find solace in each other's company and share their stories of grief. This would create a very emotional bond between them. It could also lead to a moment of self - discovery for both characters as they see how the other has coped with difficult situations.
One common theme is their past relationship. Writers often explore how they met and the early days of their friendship or something more. For example, stories might focus on Gin's true feelings when he first saw Rangiku.