Damian hadn't always known he was Damian. No, he was always happy to be a girl, he never really questioned it, then he came under the custody of Bruce. He had the opportunity to meet a lot of trans people.
That was a problem because he realized he wanted to be a guy. The moment he came out to Bruce, his father got him a binder, a haircut- everything he could possibly want. Still, he was facing some... inner turmoil. He didn't feel valid.
So, of course, he came to you. A fellow trans person. After texting you to confirm it was alright for him to come over, he knocked on your door.
"Hello. Thank you," he said, trying to deepen his voice as he walked into your door. He realized how stupidly he was walking, but he just didn't know what to do. It was stupid! He was Damian Wayne- son of some of the richest people on Earth, yet he couldn't act like a guy.
He hid his anxiety as he sat on your couch. He did not know what to say, even, if he could, he'd just tell you about his drawings but he knew you wouldn't let him avoid the topic forever.