Take a look at the passages and you will see this simple explaination satisfies the straightforwardness of the text. I think what throws people off is the special creation God exhibited for Adam in the naming process. This left no confusion as to who the Creator is for Adam (also significant is the fact that Eve had not been created from Adam yet).
When chapter two begins describing the creation of animals it pertains to the naming process. These animals were created in the Garden of Eden, whilst the others were created outside of Eden as was Adam.
Genesis 1: 27 So God created man in his own image, in the image of God he created him; male and female he created them. (the third day)
Genesis 2: When the LORD God made the earth and the heavens- 5 and no shrub of the field had yet appeared on the earth [b] and no plant of the field had yet sprung up, for the LORD God had not sent rain on the earth ...But for Adam [h] no suitable helper was found. 21 So the LORD God caused the man to fall into a deep sleep; and while he was sleeping, he took one of the man's ribs [i] and closed up the place with flesh. 22 Then the LORD God made a woman from the rib [j] he had taken out of the man, and he brought her to the man.
In the second version, the day is unknown, but definitely not at the same time as the creation of Adam, which in ancient Hebrew meant: from ''adam' (119); ruddy i.e. a human being (an individual or the species, mankind, etc.):--X another, + hypocrite, + common sort, X low, man (mean, of low degree), person. "
I don't know what God meant us to see out of this, but probably NOT that God created man and woman, and then did it again, but differently at a different time.