What does Genesis 2:20 mean?
In the previous verse, God brought the animals to the man in order for him to name them. Whatever the man called them, God allowed that to stand as their name. This is a sign of great honor, since naming something in biblical times was a sign of ownership and authority. God also seems to be taking pleasure in watching man use the intellect and creativity which makes him unique in creation (Genesis 1:26-27). The man gives names to all the livestock, birds, and wild animals.And then, in this verse, the Bible calls the man by his name for the first time: Adam. Up until now, this unique creature has been referred to as hā' ā'dām, literally meaning "the man." This name reflects the dust from which we were formed: the Hebrew word for "ground" is adamah. Here, however, the first human being is simply referred to as ā'dām, literally "Man," now taking on the nature of a personal name.
The story-sense of verses 19 and 20 is that, as Adam was naming the animals and birds, he was looking for one that might serve as his helper and companion. It becomes clear that none of the animals are suitable (Genesis 2:20). Adam needed someone who would "correspond" to him (Genesis 2:18). The fact that no animal suits this purpose is an important aspect of Scripture: humanity is truly distinctive, and meant for a truly unique relationship with other people.