Those who reject God and embrace evil, or specifically Satan, would be Satan's angels, commonly referred to as Satan's minions by Christians. Eternal judgment is not mine to make, obviously. But simply trying to understand it, I'm not so certain that there is a group who are "only" separated eternally from the face of God.
However, since God is love, being separated from God for eternity may well represent the lake of fire in and of itself. In the absence of love what is left? I don't think indifference is there, only hate. That sounds like a lake of fire to me.