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

In Genesis 2:15 God put man in the newly created Garden of Eden to work in it and to take care of it.  Early in Genesis 1:28 he told Adam to "subdue" and "rule" over the living creatures.

"Subdue" (Hebrew, kabash) means "to make it work for you."  "Rule" (Hebrew, radah) means to "dominate, be the boss."

So as the boss, Adam's first job was to give names to the creatures.  God didn't name them.  Man did.  This gave man a sense of ownership to the earth.

On a side note, did Adam name EVERY creature on the earth?  He states he named every creature in the Garden.  Not every creature on the earth would be in this garden, since it was located in the Middle East and not all creatures are there.  Polar Bears could have been named later by men who ventured out and discovered new species.  We are finding new species today and naming them ourselves.