I think I have misunderstood that verse.  When I was a kid I thought it meant that Adam named this animal “cow” and that animal “dog” and the next “cat”.

But that lacks poetry and a deeper meaning.  God intended Man to be the namer of animals, true, but not in the manner I thought.  Not “dog” or “cat”, but “Doug” or “Fluffy”.

Something happens when we give an animal a name.  They stop being an object and start becoming a subject.  Their personality and individuality blooms.