The child in the movie "The Omen" did appear sweet and harmless. Despite the true meaning, however, the baby in the film was pure evil, and the association stuck. Damian was and is a rather unused name, and "The Omen" is a very famous horror film, so many people (myself incuded) wouldn't dream of using the name because of the character in the movie.
It really is just a name, though. But a name that now carries a heavy burden of bad association.