Dear Rusty
I have not studied this subject yet, but as I understand it Casalini sold their cars in Italy under their own name, and in France they were sold through Willam. Willam was the Lambretta sales agent for France and sold vehicles made by BMA, Casalini, Decsa , Lawil, and others, all under the Willam name.
I am unsure about what name Casalini sold under in any other market, such as Holland or Belgium, as compared to France and Italy they were a smaller market. I am sure some of our Dutch friends will fill in the information gaps.
I do hope that helps you.
Chris Thomas