Damien Thorn: Why? Why me?
Damien Thorn: Why are you running away from me, Mark?
Mark Thorn: I know who you are.
Damien Thorn: You do?
Damien Thorn: Yes. Born in the image of the greatest power in the world! The Desolate One. Desolate because his greatness was taken from him and he was cast down. But he has risen, Mark, in me.
Dr. Kane: Hello, Ben? I need to see you urgently can I come down? No-no, there is something here that I just don't understand.
Dr. Charles Warren: Richard, you know me to be a rational man, but what I'm about to tell you is not rational.
Paul Buher: Do you know what exactly I do for Thorn Industries?
Damien Thorn: Not really, Sir.
Paul Buher: You should. You should know everything about the Thorn business. After all it will be yours one day.
Damien Thorn: And Mark's.
Paul Buher: And Mark's. Of course.
Ann Thorn: What are you doing?
Richard Thorn: The daggers must be here somewhere.
Ann Thorn: What you want them for? No! No.
Richard Thorn: He's not human.
Ann Thorn: He's your brother's son, he's a boy you've loved for seven years.
Richard Thorn: The boy has got to die.
Answer: Having lived as a "normal" boy, Damien is initially shocked to learn his true identity. After having time to adjust and being surrounded and groomed by satanic supporters, he eventually embraces his true persona.
The answer is correct, and I'm just going a into a bit more detail. During the events of the first film, Damien is normal until Mrs Baylock entered his life. She started teaching him about who he was, but he was only five or six, which would have been far too young for him to understand. He started acting more malicious after this point. After the movie ended, it skips ahead to Damien living with his uncle, aunt, and cousin. During that time, it's conceivable that the forces surrounding him decided to give him a period of peace. He was raised by his aunt (secretly a Satanist), but she might have been instructed to give him a normal upbringing so he wouldn't call attention to himself. As a result, he probably forgot about it, and started to believe he wasn't any different. Once he learned of his unholy lineage he began to remember and eventually embrace it, especially since he had several followers (Buher, Neff, and many others he may not have met yet) to help and protect him.