I LOVE this name, it's a perfect unisex name and so unique. And it rolls off the tongue so nicely when you say it. I'm completely sold, I think I might have to change my name to this honestly.
When I hear this name, I first think of the surname Halcyon from Star Wars, among whose members include Jedi Masters Corran Horn and Nejaa Halcyon. Then I think of Halcyon Green from the Percy Jackson series. In both cases, Hal is used as a nickname for this name (i.e. Hal Horn, Hal Green). This is actually the first time I've ever heard it as a feminine name; I always thought it was masculine.
Ellie Goulding has an album called Halcyon. This would be very, very strange as a name. It really doesn't sound like one. The word Halcyon also means a good memory from the past.