Three of the victims were pupils aged nine or under at Covenant School, a privately run Christian school.
They were named by police as Evelyn Dieckhaus, Hallie Scruggs and William Kinney.
The adults victims were employees and named as Cynthia Peak, 61, Katherine Koonce, 60, and Mike Hill, 61.
Covenant School has about 200 students, and teaches pupils from three years old up to around 12.
Ms Peak was a substitute teacher working at the school that day. Mr Hill was a janitor and Ms Koonce is described as the Head of School on Covenant's website.