“Is the name you give your child important?”
In the beginning, names signified destiny. Adam is simply the word for “mankind”, while Eve sounds like the Hebrew for “life-giver” and resembles the word for “living”. Genesis explicitly tells us Adam named his wife Eve “because she was the mother of all living”.
Nowhere does it say God named either member of the first couple. He certainly named the species, but not the individuals. He left that up to our questionable judgment.