You could also focus on her abilities. Since Hidan is known for his immortality through his jutsu, a female Hidan could have a variation of that. Maybe her immortality is linked to a different source, like a powerful female deity in the Naruto universe. This could lead to many interesting plotlines where she has to deal with the consequences of this power and how others try to either use or destroy her because of it.
Another aspect could be her relationships. For example, how would she interact with the other Akatsuki members? She might have a different dynamic with them compared to male Hidan. She could form an unexpected friendship with one of the members, like Konan, and they could support each other in their respective goals.
One idea could be to explore her backstory. Maybe she was an outcast in her village due to her unique beliefs and fighting style, similar to Hidan in the original. She could be on a journey to find a place where she truly belongs.