Cyberpunk 2077 will let you choose your character's backstory, as well as their gender. A hands-on at E3 2018 confirmed that while your Character themselves is already set, choices you make at the beginning of the game will impact the game's story.
Andy McNamara, editor of GameInformer, tweeted earlier to say that "you are V. Can play as Male or female, and you choose your past and it affects your story." You can view that tweet towards the bottom of the article, and I'll link out to the rest of the tweets in that thread as well.
Cyberpunk will probably make it onto our list of the best RPGs.
We already knew that you'd have to play as V, but CDPR's Cyberpunk trailer from E3 2018 suggested he'd be a male character that you'd be tied to throughout the game and would have little opportunity to shape, much like Geralt, the main character from CDPR's The Witcher series. Although you have the opportunity to play Geralt in a variety of different ways, his character is largely defined by the studio, not you as a player.
McNamara's tweets confirm that you can shape the backstory of your character, which will affect the way your story plays out.