Is the name 'Tony' Italian in origin?

No, Tony is not an Italian name in terms of the spelling even though it is the English equivalent of a name whose origins are in Italy.

Specifically, the name functions most commonly as a masculine proper noun. It is a nickname for Anthony. The names reflect the English translations of the Italian nickname Toni and the Italian given name Antonio, whose origins may be Etruscan or Peloponnesian Greek.

Tony for Italians became widely popular do to Ellis Island bringing Italians and stamping To NY (To New York)