Adaar is a cannon mounted on a qunari ship?
Here's an idea. Perhaps Adaar's mother and/or father were gunners on a Qunari Dreadnought. Then they either deserted because they didn't want to be part of the Qun anymore or their dreadnought was overturned during a battle or storm with the pair being left for dead and choosing to start fresh.
However they left the Qun, they took new names for themselves, but kept Adaar as their surname so that they and their daughter/son wouldn't forget their origins or heritage. It's even possible that Adaar was a Qunari title for a Dreadnought gunner or dreadnought officer.