Many white families became closely attached to their slaves. They had no intention of the slave families being separated at the death of the owner. Estate inventories should be studied carefully for clues of family units being left intact to the widow, or to elder children. If John, the father of Elizabeth, the mother of Nicholas owned the land and then the lease expired, that would prove the relationship between the three. These deeds might also mention a power of attorney which would give a wife's maiden and married name.
Prenuptial agreements imply the existence of children.
Don't assume to much by a name without investigating several possibilities. In Virginia parent's would name their children after the surname of grandparents. If slaves received these kinds of names this could suggest white parentage to the slaves. A person could be a junior in one record and later appear as a senior in other records if the previous senior had left the county or died. Triple given names such as Raymond Thomas Johnson Green was often a naming pattern of illegitimacy.