Zanetta may come from Greek. It may be the Greek equivalent of the French
Jeannette or the Italian Giannetta. The first sound is really "Z" in Greek since Greek people would hardly pronounce the French or Italian sounds in that name.
I cannot explain while the Hungarian Zsanet would be spelled Zanetta in English. The Hungarian name is also a verson of the French
Jeannette and if someone did not like the Hungarian spelling, why not return to the original French spelling or to the English Jeannet?
The name Zanetta might also come from Poland. The Polish spelling of the French
Jeannette would be Zaneta with a special dotted Z. But why the double "t" in Polish?