That's Not My Name by Megan Lally

It was a mistake to trust him.

Shivering and bruised, a teen wakes up on the side of a dirt road with no memory of how she got there—or who she is. A passing officer takes her to the police station, and not long after, a frantic man arrives. He's been searching for her for hours. He has her school ID, her birth certificate, and even family photos.

He is her father. Her name is Mary. Or so he says.

When Lola slammed the car door and stormed off into the night, Drew thought they just needed some time to cool off. Except Lola disappeared, and the sheriff, his friends, and the whole town are convinced Drew murdered his girlfriend. Forget proving his innocence, he needs to find her before it's too late. The longer Lola is missing, the fewer leads there are to follow…and the more danger they both are in.