Genesis 2:19-20
And out of the ground the LORD God formed every beast of the field, and every fowl of the air; and brought them unto Adam to see what he would call them: and whatsoever Adam called every living creature, that was the name thereof.
And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him.

God created all the animals that lived on the earth, all the animals that lived in the sea, and all the animals that flew through the air. But He did not give them names. He left that for the man. After all, He had given the man dominion over all those animals. So why not allow him to call them whatever he chose?

By giving man the ability to name each creation in the animal kingdom, God shows man's authority over those animals. Any time someone has naming rights, they are the authority. Think about when a set of parents has a new baby. They decide what that baby will be called. They have that authority, given to them by God. Remember Daniel and his three friends? When they were taken captive, their names were changed. Daniel 1:7 says "The chief official gave them new names: to Daniel, the name Belteshazzar; to Hananiah, Shadrach; to Mishael, Meshach; and to Azariah, Abednego." Their captors took authority over them, and changed their names.

The problem remained that there was no creature suitable to be the helpmeet for the man. None of the creatures possessed the man's ability to reason and to express affection. There was an allegiance that the creatures devoted to their lord, but there was none equal to him. This was a problem that Elohim, the faithful Creator was about to solve.