With Genesis 2:19–20 it is again important to pay close attention to the context. The perspective of these verses is determined by Genesis 2:18. The Lord wants Adam to discover for himself that it is good to have a helper. He wants to awaken the desire for that in Adam.
This verse does not tell us that the Lord made man first and then the animals. What we read here is a reference back to the creation of the animals as we read about it in Genesis 1:1–31. Here it is recalled that the Lord made all the animals. He brings all the animals he has made to Adam.
19 Now out of the ground the LORD God had formed every beast of the field and every bird of the heavens and brought them to the man to see what he would call them. And whatever the man called every living creature, that was its name.