It wasn’t supposed to be a secret.
If you died while with the league, you will no longer be acknowledged to have existed, especially if you died during a mission. A disappointment will not be remembered.
The bats and birds don’t like speaking about the people they have lost, so they don’t. If someone ask about the dead, they will tell the person they don’t talk about that.
So how was Damian supposed to know that he should have told his father about his dead brother?