Name of this Italian pastry?
I don't think these have a specific name, but it's possible to take a guess what they are made of.

The container is a "cialda", a thin waffle. Here is a recipe with pictures, basically it's done with a waffle iron with shallow ridges.

The cup is also lined with dark chocolate - the rough appearance suggests this was made in the shop and not bought already made.

What is inside is the hardest to guess, but I think it's likely some pistachio-flavoured "crema pasticcera", pastry cream. Likely milk (possibly also cream), sugar, pistachio paste, egg yolks, rice and corn starch. 

The topping is made of crushed nuts, I'd say pistachios but the picture is too small to be sure.