Answers (in order)
Mike Piazza (Piazza means "public square" in Italian, though the largest one in Italy is round, as is the most famous one - St. Peter's Square in Rome.
Joe Dimaggio (Magggio is the month of May and "di" means "of")
Mike Napoli (the Italian name of the city that invented pizza).
John Boccabella (Boca is mouth, bella is pretty)
Biff Pocoroba (poco is not much or few, roba is clothes, sometimes used the way we use "stuff" in English to mean things)
Dave Righetti (righe are lines)
Vincent Dimaggio
Dominque Dimaggio (Dominique means "of the lord")
Rico Petrocelli (Rico means "rich" as in wealthy in Itailan and petra is rock - "elli" is plural and is a suffix making a word diminutive (should have read "Rich Little Stones" not stone)
Joe Torre (tower in Italian