Halvey is an Irish surname originating in an area near the Black Sea. The clan then moved to Spain where they took part in the Spanish Armada. Due to rough seas, the clan landed of the west of Ireland in 1588 where they settled.
Since then many generations migrated to the USA and some to Great Britain due to poor economic conditions in the country. To this day many Halveys are found in County Wexford and County Galway in the Republic of Ireland.
References
Halvey Wikipedia(Text) CC BY-SA