Y/N has powers and when she told her parents they promised they would help her but when they get out of control they throw her out. Ever since than it's been difficult for her to trust anyone. So when she meets Peter she can instantly see that he's a trickster and he uses people's secrets against them. Y/N decides to lie about everything including her name. Peter knows she's lying so he tries everything he can to get her to tell the truth but it never works.
I know the story doesn't follow the plot line of Once Upon A Time because I decided to do my own version.