Spoiler!! Mido's name

At the start Oh Dae-su is on the phone talking to his daughter. He mentions an entirely different name. He refers to her as Yeun-hee. If I remember the plot itself correctly, I think Mido was also hypnotised. She probably had memories of her old name erased somehow and then became known as Mido.

I love this movie, it may even be one of my favorites, but that just bugged me. So thank you for clearing that up.