Torriani is not a particularly rare name, in Italy and particularly in Lombardy. My mother's family name is Torriani, but their specific records only go back fully to the mid 18th century. They probably came from Northern Lombardy. Bear in mind that Ticino (long a part of Switzerland) was in the middle ages often part of the Duchy of Milan. One Torriani family indeed ruled Milan, but it is somewhat unlikely that many of the people now called Torriani descend directly from them; they were largely salughtered by the Visconti family, who in turn were polished off by the Sforza family. It was a remarkably nasty part of history, lots of assassinations, etc. The last of the ruling Torriani was, i believe, placed in a cage high on the Ducal castle walls and left to slowly starve in full view! Napo Torriani was an archbishop, if i recall correctly, and ruler of Milan for a while (at that time temporal and church authority was often intermingled). There are still quite a few Torriani in Milan.