I really like it. The meaning "tamer" or "soother" is calming and reminds me of tension tamer tea blends that are supposed to relieve stress. The sound is modern, but the name is not over used.
There were several saints or
Christian figures named
Damian, and it also reminds me of
Damian Wayne (Batman's son) and
Damian McGinty (an Irish singer). Regretfully a few people I know associate it with the horror film. Both a family member and a co-worker/friend automatically thought of the "Omen" when I mentioned
Damian in the past. I've never watched the "Omen," but it is significant that a certain age group seems to automatically be reminded of the movie.