She changes it a great deal. For starters, the gender difference can bring in a new type of relationship. Instead of the more traditional male - male rivalry, there could be an element of attraction or different kind of respect. Also, her way of handling the Force and Jedi teachings might be different, which would affect how Vader reacts to her.
One interesting idea could be a female Obi - Wan being a mentor to a younger generation in a different way than the male Obi - Wan. She might use her unique perspective to train Jedi. As for Vader, a fanfiction could explore his relationship with this female Obi - Wan in a more complex way, like they have a grudging respect for each other's skills.
One possible plot could be that Vader, without his suit, is found by Obi - Wan in a hidden location. Obi - Wan, despite their past, decides to help Vader recover. As they interact, they start to understand each other's perspectives better. Maybe they even form an uneasy alliance against a new common enemy in the galaxy.
Their relationship might start with suspicion. Obi - Wan would be cautious as he's seen Vader's evil deeds. But as Vader is suitless and perhaps more 'human' in a sense, Obi - Wan could start to see the Anakin he once knew. This could lead to a slow rebuilding of trust.
The most obvious implication is the destruction of Obi - Wan's world. Obi - Wan would be devastated and likely turn all his efforts towards revenge. This would change his character from a calm and collected Jedi to a more vengeful figure.
Some fanfictions might explore a situation where Anakin is being manipulated by a powerful dark force or a Sith Lord. This dark influence makes him see Obi - Wan as a threat to a grander plan. So, he kills Obi - Wan as part of this dark scheme, not fully in control of his own actions. And this can lead to a lot of complex emotions and plot developments later in the story, like Anakin's further descent into darkness and how the other characters react to Obi - Wan's death.
In fanfiction, we can also see how an OC might change the power balance between Vader and Sidious. If the OC is a powerful ally to Vader, it could lead to a split in the Sith order. Or if the OC is a double - agent working for both, it can create a complex web of lies and deceptions that make for a very engaging read.
One great aspect of fanfiction involving Darth Vader, Darth Sidious and an Original Character (OC) is the potential for new storylines. For example, an OC could be a Jedi who manages to infiltrate the Sith ranks, interacting with Vader and Sidious in unexpected ways. This could lead to intense power struggles and moral dilemmas within the story.