Kay

Along with what pinklight and genwall have said about naming, I’d like to bring out a point Frank made in his comment #11:
“When God created Adam he made this one in the image of God. Male and female he created them, and he blessed them and named them Adam when they were created.”

“Adam” is a term for both of them – it’s not just the first male’s given name. In Gen.5:1:
“This is the book of the generations of Adam. In the day when God created man, He made him in the likeness of God.”
-the word translated as “Adam” in the first sentence is the exact same word translated “man” in the second.
Eve was “named” woman and she was “Adam” along with the man.

Another interesting translation tidbit is that the exact same word ‘ishshah’ translated “woman” in verse 23 is translated as “wife” in verse 24.