The name Monica is a Greek baby name. In Greek the meaning of the name Monica is: Alone. Advisor. Latin Meaning: The name Monica is a Latin baby name. In Latin the meaning of the name Monica is: To advise.Counselor.Spanish Meaning: The name Monica is a Spanish baby name. In Spanish the meaning of the name Monica is: Advisor.n Greek the meaning of the name Monica is: Alone. Advisor. Latin Meaning: The name Monica is a Latin baby name. In Latin the meaning of the name Monica is: To advise.