Kay

“Adam identifies the animals before the woman is created, but he doesn’t name them, or give them names like “Tommy the cat”, “Leo the lion”, or “Sparky the dog.” The woman’s name was never “Woman”. Her name was Eve, not “woman”. There is a difference between naming a creature and identifying or recognizing one.”

Well put, pinklight!

“I think PL is onto something here. Why were the animals brought to Adam in the first place? Was it so he could exercise dominion over them in some way?”
No, gengwall,
it certainly doesn’t read that way to me. I think you are right on with:
“Finally! Here is one like me”. That makes “she shall be called woman” not an act of authority but a proclamation of great joy.”