It looks like an exceedingly kreaytif version of Deirdre to me. It took me a LONG time to realize the name wasn't spelled "Deidre," which is why I suspect someone else might not have caught on, either. :)
Otherwise, it could be a combination of the prefix "de-" with a name based off of Adria or Adrian (or something similar). I don't suppose you've got more info on the name?
"What are these parents thinking?...Let's name her Madison--she'll live in her own world: 16 square miles surrounded by reality." -- Susan Lampert Smith