Genesis 2:20b but for Adam there was not found an help meet for him.
21: And the LORD God caused a deep sleep to fall upon Adam and he slept: and he took one of his ribs, and closed up the flesh instead thereof;
22: And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.
23: And Adam said, This is now bone of my bones, and flesh of my flesh: she shall be called Woman, because she was taken out of Man.

In the beginning, God created the woman, or Adam's wife from the rib of Adam.  She was to be a help suitable for him.  Just what he needed.  It was Adam who gave his wife her name.  Much as it is today in marriage.  The woman takes on the name that her husband gives to her.    The scripture said in God's "eye-view"
they were called Adam.  She was not, from the beginning, to rule over her husband.  It was at Eve's suggestion that Adam took a bite of the forbidden fruit..  Had Adam thought through his command from God, he would have rebuked his wife, who was to help him, not to bring him down.

3:20: And Adam called his wife's name Eve; because she was the mother of all living.

  Gen:5:2: Male and female created he them; and blessed them, and
called their name Adam, in the day when they were created.

In this state, the woman in submission to her husband, God blessed them.  As long as she was of