This phrasal verb has a lot of meanings
1. Give sth away = 1.1 Give something as present.
1.2 Tell something about somebody. (as a secret)
She gives me away a ring in my birthday.
He gives me away that he has a lover.
Give sb away = betray to someone.
They give the rapist away.
Give yourself away = betray yourself.
You gave yourself away when you said it.
He gave yourself away in the exam because he took off a paper with the answers of his bag.