If I remember correctly when he posted it to usenet it was:

    P = Practical
    E = Extraction
        and
    R = Reporting
    L = Language

From the Original comp.sources.unix SHAR file:

    X.TH PERL 1 LOCAL 
    X.SH NAME 
    Xperl - Practical Extraction and Report Language 
    X.SH SYNOPSIS 
    X.B perl [options] filename args 

He wanted it to be short because he was going to type it a lot. He wanted it unique so that he could use grep to locate all Usenet discussion on it in all newsgroups. (Yes, he was pulling the Kibo trick.) And what sold him on whimsical was the presence of the 2 different possible acronyms: Practical Extraction and Reporting Language, Perfectly Eclectic Rubbish Lister. He therefore included both in the documentation from day 1.

Larry himself is not particularly dogmatic on the capitalization. But as you can see in the link you posted to his original Usenet post he did not think of it as an acronym. He was at that point capitalizing it Perl or perl depending on where it appeared in the sentence.

However long ago the capitalization of the language became a litmus test for whether you had exposure to the community. See http://www.perlmonks.org/?node_id=510594 for evidence of that.

  $ perldoc perl | tail -n 14

         Perl actually stands for Pathologically Eclectic Rubbish Lister, but
         don't tell anyone I said that.

  NOTES
         The Perl motto is "There's more than one way to do it."  Divining how
         many more is left as an exercise to the reader.

         The three principal virtues of a programmer are Laziness, Impatience,
         and Hubris.  See the Camel Book for why.



  perl v5.14.2                      2012-07-12                           PERL(1)

In conversation with Larry Wall I found out that the existence of two reasonable backronyms was part of why he chose to call it Perl. Therefore the backronyms were known before the name itself was finalized.

Interesting...

And yes, I've heard the Pearl claim before. As well as the claim that the original acronym was going to be Practical Extraction And Reporting Language.

All of the claims that I have heard fit together if you assume that the actual sequence of events was this. Larry wanted to name it pearl for whatever combination of reasons. Came up with a nice acronym for it. Decided not to name it pearl for whatever combinations of reasons. Was playing around and came up with the Perfectly Eclectic Rubbish Lister. Preferred that over pearl for various reasons (not in use, greppable, likes puns, etc). And therefore named the language perl. Therefore the language name is not an acronym, but both popular backronyms predate the actual language name.

I was not present. But this is my best guess as to what did happen.