The Genesis account of creation is breathtakingly sparse. Yet what little it does say causes us to think deeply because we want to know the whys and wherefores, the details as well as the overall scheme of things. The section you ask about has, within its own record, two main points that answer the question.
First, God was communicating openly with Adam so that Adam understood all he needed to understand as a directly created human. He understood God's commission to be a horticulturalist (tending the garden) as well as a zoologist (naming the animals). Notice how God brought all the animals to be named TO Adam? He was not left to get on with such a monumental task without God's instructions and enabling. Further, that task caused Adam to realise he had no mate, as did all the creatures he named. That was deliberate, on God's part, for only when humans discover a lack might they look to God to fill it. And he did - deliberately, not accidentally.
Second, Notice how, as with the animals, God brought the woman TO Adam? And Adam called her 'woman'. (He did not name her 'Eve' until after God had promised the then-sinful couple that she would be the mother of all living.)
So with the woman. After Adam regained consciousness, God presented her to him and immediately Adam recognised in her the mate, the companion, the one like him who had been lacking up until then. He knew God had formed her from himself because she was so strikingly similar to himself, unlike any of the animals. And - although this next point is my personal opinion - whenever I think of human likeness, I think of DNA, and is not bone marrow full of DNA? The Creator only needs to tweek human DNA a tiny bit to produce whatever variations he so desires - including the female variation.
But just as there is no scientific language in the creation account, there are no detailed minutes of the meetings between God and Adam - just the over-view. Minutes are not a record of all conversations between the gathered parties, only of the decisions and conclusions arrived at. Consider those opening chapters of Genesis as the minute of that interaction between God, Adam, and the woman, and dwell on the conclusions provided, so that we can move forward in the will of God.