Greek Meaning: The name Stacey is a Greek baby name. In Greek the meaning of the name Stacey is: Fruitful, productive. Famous bearer: St Eustace (Eustachins) was a martyred 2nd century Roman soldier.American Meaning: The name Stacey is an American baby name. In American the meaning of the name Stacey is: Fruitful, productive.Famous bearer: St Eustace (Eustachins) was a martyred 2nd century Roman soldier. English Meaning: The name Stacey is an English baby name.merican Meaning: The name Stacey is an American baby name. In American the meaning of the name Stacey is: Fruitful, productive. Famous bearer: St Eustace (Eustachins) was a martyred 2nd century Roman soldier. English Meaning: The name Stacey is an English baby name.