It's a tad overdone in the gourmet stakes and seems a bit porny. I came across a Delysia in a newspaper column, born around 1930 I'd guess - that's at least a prettier spelling.
A fictional person with this name was Amy Adams' character in the 2008 film, Miss Pettigrew Lives for a Day. Only it was spelled "Delysia".
I agree there's a cannibalistic element to this name that's just off. I can't picture any parent naming a child this; it's better as a stage name chosen by an adult!