Little to nothing is known about Becky, though she does seem to show a number of psychotic symptoms. She is shown to enjoy violence and seems to be difficult to control, even for a capable leader. She also has little to no fear of death and doesn't seem to react to dangerous situations in a normal manner, seeing them as more exciting than fearsome.
Behind the scenes
Becky was based on the author's friend from high school, in terms of her name and aesthetic design. She was done up to be similar to the Joker from Batman as this was the friend's favourite character.
Her personality, however, is not based on anyone.