(January 2013). Beech Island is an unincorporated community of Aiken County, South Carolina in the United States. It appears to take its name from Beech Island, a nearby former island that is politically part of Georgia but geographically separated from the rest of Georgia by a river which changed its bed.It was preceded by the trading post and fort at Savannah Town.eech Island was primarily an agricultural community before the 1950s. Cotton, wheat, corn, and soybean were the major crops. This changed with the construction of Urquhart Station Power Station and the nearby Savannah River Nuclear Project.