This cocktail dates back to the 1940s and therefore its somewhat unfortunate name is a reference to the film and play of the same name. But that begin said, this drink's memorable name [really?] and appearance [a slight shade of purple blue] and distinctive nose [absinthe and violet!] means that few who have it do not remember it.
I think this is a pretty stunning drink when made well. You need to have a good quality mixing Absinthe. I like Leopold Brothers' later batches for this, though your mileage may vary here. The absinthe can dominate this cocktail, so be wary and choose prudently. Secondly, I like a bit more Creme De Violette than some of the other canonical recipes. I think that if its too dialed back, you end up with a tad too much anise.
In terms of gins, you can't go wrong here. A nice floral contemporary gin I think brings out the best results. For an interesting twist, a contemporary herbal gin like Gin Mare really changes the feel of this drink. I'd only recommend staying clear of most Navy Strength gins as they have a tendency to team up with the Absinthe creating a domineering and overwhelming heat that kills the subtle notes which make this cocktail work.