So, after a talk with a friend of mine, it seems there are:
Piccinino: a very joung person, used to be child 7-10 years old, that started to learn the job. I do think it does not exist anymore in Europe.
After 3 or 4 years of practice he became:
Mezzo Lavorante: person who take the different pieces of the jacket and prepare it for the first or the second trying-on
Lavorante: the person who finishes the jacket after the second trying on.
I think you could translate trimmer as: Lavorante
and cutter as: Tagliatore.