Eve unnames them

1.God and the Universe
"You and your father lent me this- gave it to me, actually. It's been really uselful, but it doesn't seem to fit very well lately"
While there is a God mentioned in this story, he does not seem to possess any power over creation. It seems as if Eve has the self given power to do as she wishes, which in this case is to unname everything.

2.Humanity and Identity
"...they understood that the issue was precisely one of individual choice, and that anybody who wanted to be called Rover, or Froufrou, or Polly, or even Birdie in the personal sense, was perfectly free to do so..."
Ultimately you make yourself out to be as you want to be seen. A name has no meaning and if you do call yourself by a name, you can determine your own meaning. Whatever you think is right, is right.

3.Conflict and Suffering
"They seemed far closer than when their names had stood between myself and them like a clear barrier..."
The conflict is trying to overcome the "barrier" that names set in place among every living thing. There is no mention of flaws.

4.Hope and Redemption
"It is hard giving back a gift without sounding peevish or ungrateful"
The answer to the human struggle is that we must rid ourselves of the world's given titles and names and simply be. After we eliminate the "barriers" we can find hope in simply living as we believe is right.

5.Values and Relationships
"One of my reasons for doing what I did was that talk was getting us nowhere..."
The words that are used in the world do not have a set meaning. Just like our names they are ultimately pointless. Therefore we cannot find a set way to live. We can only follow the path that we believe to be correct.

6.Truth and Reality
"I could not chatter away as I used to do, taking it all for granted"
Words and more specifically names have no real, absolute meaning. Whatever you want to believe is the truth and there is no need for names or words. They just get in the way of how we relate with one another.

Therefore, after answering the questions for the above topics, I believe that She unnames them expresses a postmodern worldview.