Craig

I am not sure that in most comps’ minds that the naming of a species or category rather than an individual would be any less of an indication to them of authority. For example, they would say that Adam could name tigers because he had authority over tigers.
This argument

Naming someone does not establish, express, or validate any authority that doesn’t already exist. Nor is the presence of an authoritarian hierarchy necessary to give a name.

seems a stronger argument to me. Thus Hagar could give God a name later on in Genesis.
If this is true, then Adam naming Eve after the fall wouldn’t have necessarily shown his post-fall rulership either.