I think by now plenty of people know about it through word of mouth. They told a friend, that friend had to explain it to a family member, that family member mentioned it at the tavern, etc.
I can see a pretty even split on how the DKs themselves handle sharing it. Some might be ashamed, or not want to talk about it for fear of tempting themselves in a place where it’s not appropriate, or just don’t want to frighten people. They won’t lie about it and will discuss it if asked, but won’t bring it up for no reason. The sort who want to fit in with the living.
Other more aggressive, less-social types might use it as an intimidation tactic. “I haven’t drawn any blood yet today, so who knows what I might do if you continue talking?”
There may even be a bit of contention between the two types. One side accuses the other of being too soft and gentle, inviting the potential for danger because people don’t understand how dangerous they are if you hide it. The other side is accused of being needlessly aggressive, making them look like monsters, and alienating them from the living.