Is Arya Stark became Faceless Men ?

Arya spent the past couple years in the free city of Braavos training to be a Faceless Men. But it was never cleared if she became a Faceless Men or not. Before she left Braavos Jaqen told her "Finally a girl is no one", and we also have seen her taking new faces when she killed Walder Frey. But we saw her introducing herself as Arya of House Stark which doesn't sound like something a Faceless Men would say. So there are two theories, one is Arya killed the Waif and became a Faceless Men and another one is she was killed by Waif, and it's Waif wearing Arya Starks Face. I guess we would never know this for sure.