Naming can be and is an act of dominion on occasion. For example, if the name-giver is God, a patriarch, or a king, the name given is part of the intention to shape the destiny of the one named. We see this in the naming of Abraham or Jacob/Israel. Or again, in the naming that goes on in families upon the birth of a child, we see the authority of the parent expressed and the expectation for the child encapsulated in the name. For example, we might think of the naming of Jesus in this regard.
In attempting to subvert the order of creation, feminist interpretation of Genesis 2 asserts that Adam had no dominion or rule over his wife until after the Fall. The proposal is made therefore that in the New Creation, we should return to the ideal of Eden in which the man and the woman are equal as to role. Such an argument neglects to see or deliberately puts aside the teaching implicit in Adam’s naming of Eve and the cultural significance that such naming carried in patriarchal times. The naming shows that Adam had authority over Eve. The harmonization of Genesis 1 and 2 in this regard would see Eve’s authority in creation as derived from her husband.