Gaines' Mill was a Confederate victory.
If you mean, however, which name is northern and which southern, Chickahominy would be the northern name; the Chickahominy is a river on the Peninsula and generally flows from northwest to southeast until flowing into the James River. Gaines' Mill was a gristmill owned by Dr. William G. Gaines, a prominent landowner and ardent supporter of the Confederacy. It stood about a mile away from the battlefield but was apparently the most prominent structure for the Confederates to use for naming.