Gen 16:13-14 [Hagar] gave this name to the LORD who spoke to her: “You are the God who sees me,” for she said, “I have now seen the One who sees me.” That is why the well was called Beer Lahai Roi; it is still there, between Kadesh and Bered.
Here we have Hagar giving Yahweh a name – a name recorded in Scripture. (The well is also then called by this significant name.)
Clearly, naming does not necessarily imply authority.
Even if, for some reason, you do not accept the above, you have to remember that God did not tell Adam to name Eve. God named both Adam (Gen. 5:2), but the male Adam then chose to rename the female Adam. If you believe Adam used authority in naming, he usurped authority that belonged to God.