"Now the LORD God had formed out of the ground all the beasts of the field and all the birds of the air. He brought them to the man to see what he would name them; and whatever the man called each living creature, that was its name. So the man gave names to all the livestock, the birds of the air and all the beasts of the field." Genesis 2:19-20 NIV
In the midst of extending his creation of man from just male to male and female, God brought Eden's menagerie before Adam, sat back so to speak, and let man take the lead in something creative. Some might find fault with my characterization of this event this way, but I don't think it's all that far off.
This occurred before God's sabbath, so his "work" week wasn't quite finished when this happened. He was, in fact, not even done with the model called man, for female he had not made them yet. He tapped his son Adam to help his Dad finish his work, much the same way my dad used to "take me to work" with him on Saturday mornings to "help" him. Day 6 was the very first Take-Your-Son-to-Work Day in history!
The work wasn't hard (neither was mine with my dad). The Father could easily have done it himself, but he didn't want to. In fact, it seems to me, the Father got a kick out of having Adam do it. I know it doesn't come right out and say that, but it does say God went on to finish his creative work (including the part Adam "helped" with), and when done, pronounced it good. A perfect God produced perfect quality work with which he was perfectly satisfied--including the component added by Adam!
One might ask, "Why?" I think it speaks profoundly about the glory of God and what brings him satisfication and joy. The news flash is that it isn't doing a puppet show with the marionettes he made out of clay. God let man name the animals, and whatever man named them, that was their name.
God wanted mankind to be creatively free. He made them to be. That is what they must be, in order for the Son to incarnate as one of them and fellowship with them, Creator with the created. God has never shown any interest in dealing with mankind as robots so far as I can tell: it is a complete misapprehension of his purposes and plans to ever think that he would.