Movie about a house haunted by a teenage girl who possesses the daughter

Question

I believe it's only the mom and the daughter who move to a new house. The house is haunted by a teenage girl who died there and now she wants to possess the daughter. The ghost ends up succeeding, but the mom figures it out though when she asks her "daughter" where she came up with her name and the ghost can't answer her or doesn't answer correctly.

Answer 1

It's Secrets in the Walls (2010)

In IMDB:

How does the movie end? Now believing that Greta has possessed Lizzie's body, Rachel pretends not to know and invites "Lizzie" to go house-hunting with her. On the way, she stops at the house to pick up a trunk. Greta/Lizzie is apprehensive about going in the house, but she eventually agrees to help Rachel carry it out to the car. Once inside, Rachel asks Greta/Lizzie whether she remembers why she was named Lizzie. When Greta/Lizzie can't answer, Rachel confronts her, and they begin to struggle. In the fight, Greta/Lizzie falls down the staircase, and the necklace is knocked off her neck, allowing Lizzie's spirit to re-enter her body. When she comes to, Lizzie answers the question. "You named me Elizabeth because she was strong," Mother and daughter hug. Some days later, as Rachel, Lizzie, and Molly are moving out of the house and the realtor is showing it to a new family, Rachel attempts to warn the family that the house is haunted but the husband says that they don't believe in ghosts. "You should," Rachel replies. In the final scene, as the prospective buyers enter the house, telling the realtor that they have two teenage daughters, Greta can be seen looking out of an upstairs window.