English Meaning: The name Antony is an English baby name. In English the meaning of the name Antony is: Highly praiseworthy. From a Roman clan name. In the 17th century, the spelling Anthony was associated with the Greek anthos meaning flower.Italian Meaning: The name Antony is an Italian baby name.merican Meaning: The name Antony is an American baby name. In American the meaning of the name Antony is: Priceless. Latin Meaning: The name Antony is a Latin baby name. In Latin the meaning of the name Antony is: Worthy of praise; of value.