Rebecca Mitchell is a character in DEXTER. A girl cut off from the rest of the world at home, she is the daughter of Arthur Mitchell and Sally Mitchell while also being the younger sister to Jonah Mitchell. Because of the solitude forced on her by her father, she apparently lacks awareness of social norms, which leads her to inappropriately flirt with Dexter Morgan. Unfortunately she is just another victim in Arthur's madness, often referred to as "Vera Mitchell" rather than by her real name and treated so protectively just like Arthur wanted for his sister.
After Arthur's "disappearance", she and the family are put into protective custody and eventually move to Kearney, Nebraska where she is forced to live under the constant complaint of her deranged mother who blames both of her children for the way Arthur was. Her praise for him and desire to be whisked away eventually drove Rebecca to suicide, resulting in her brother turning his rage on his mother effectively killing her in the process. Jonah covered this up as a killing of Trinity and ultimately was left for his own choices by Dexter, who intended to kill him but discovered the remorse and light in his life while also comparing Jonah to his own son Harrison Morgan.
Season Four
Though she is a teenager her room resembles that of a young girl's. After running away once, Arthur now has locks on the outside of the door and on the windows. Arthur sometimes calls her "Vera", in the name of his deceased sister. When Dexter asks her about this and tries to console her, she asks him to take her away, implying she will give him sexual favors to do so (which Dexter flatly refuses). Becca refuses to believe that Dexter wants nothing from her. Upon catching Becca's advances on Dexter, her mother only cares about Arthur never finding out, despite her assumption that Dexter has/will have sex with her daughter.
It is implied that Arthur Mitchell likely sexually abuses her, due to her offer of sexual favors to Dexter, her assuming that this is "what all guys want", and her mother's general indifference to her daughter's sexual behavior.
Season Six
In Season Six, it is revealed that she, along with her mother, Sally Mitchell, were killed by "Trinity", despite his death at Dexter's hands.
Rebacca's Death, seen on Dexter's computer, in FBI database
Dexter believed it was her brother, Jonah. However it was not Jonah who killed Rebecca, her mother blamed the kids for what Arthur was. Becca finally had enough of it and killed herself in the bathtub in the same fashion that the Trinity Killer killed his bathtub victims, and Jonah lost his temper on his mother and killed her.