Long long ago, Larry famously wrote a short and handy rename Perl script (which seems to have been lost). However, improved versions of this script can still be found. See for example:

• rename 0.3 - now with two extra cupholders (by Aristotle)
• File::Rename (CPAN module)
• perl rename question (SO question)
• Perl Rename by Mad_Mac and response Re^3: Perl Rename by afoken (2010)

I'm pretty sure I've been schlepping this one along in my homedir as ~/bin/rename for well over two decades now that's genesis is about six years after the original.

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The cake is a lie.
The cake is a lie.
The cake is a lie.

That may not work correctly, depending on what characters are in the file name:

$ ls -l
total 0
-rw-r--r-- 1 john john 0 Feb  1 20:23 four
-rw-r--r-- 1 john john 0 Feb  1 20:23 one
-rw-r--r-- 1 john john 0 Feb  1 20:23 two ? three
$ ls | perl -nle 'BEGIN { $counter = 0 }; $old = $_; $new = "caption" 
+. "$counter" . ".txt"; rename( $old, $new ); $counter++;'
$ ls -l
total 0
-rw-r--r-- 1 john john 0 Feb  1 20:23 caption0.txt
-rw-r--r-- 1 john john 0 Feb  1 20:23 caption1.txt
-rw-r--r-- 1 john john 0 Feb  1 20:23 two ? three
[download]

Better to use perl's built-in glob function:

$ ls -l
total 0
-rw-r--r-- 1 john john 0 Feb  1 20:28 four
-rw-r--r-- 1 john john 0 Feb  1 20:28 one
-rw-r--r-- 1 john john 0 Feb  1 20:28 two ? three
$ perl -e '$counter = 0; for ( <*> ) { $old = $_; $new = "caption" . "
+$counter" . ".txt"; rename( $old, $new ); $counter++; }'
$ ls -l
total 0
-rw-r--r-- 1 john john 0 Feb  1 20:28 caption0.txt
-rw-r--r-- 1 john john 0 Feb  1 20:28 caption1.txt
-rw-r--r-- 1 john john 0 Feb  1 20:28 caption2.txt
[download]

Why needs the counter be inside a BEGIN block?

In this example, perl is reading line by line, (perl -nle ...) and you want the counter to only be initialized (once) at the start of the script.

you can avoid the oneliner BEGIN block using the Maori-farewell like in perl -M'5; $counter=0' -nle ...

But you can avoid the counter at all:

>perl  -nlE "say sprintf qq(caption%03s.txt),$count++" one.txt two.txt
+ three.txt

caption000.txt
caption001.txt
caption002.txt
[download]

PS you get the filename currently processed in $ARGV so you can play with it:

>perl -nlE "say sprintf q(caption%03s.txt),$1 if $ARGV =~ /.*([\d]+).*
+/" one01.txt one02.txt

caption001.txt
caption002.txt
[download]

PPS note that perl -n and perl -p both skip empty files!

ls -l

-rw-rw-r-- 1 io io  0 feb  2 13:28 one.txt
-rw-rw-r-- 1 io io  0 feb  2 13:28 three.txt
-rw-rw-r-- 1 io io 20 feb  2 13:37 two.txt

perl -nlE 'say "processed $ARGV" if eof' *.txt
processed two.txt
[download]

PPPS after choroba's nice below response I cant resist to update the title and to try it:

 perl -MTie::Scalar -M"5;{package SN; use parent -norequire => 'Tie::S
+tdScalar';sub FETCH {print qq(Opening ${$_[0]}); ${$_[0]}}}; tie $ARG
+V, SN" 
      -nlE "say qq(\tprocessed $ARGV) if eof" 001.txt 002.txt 003.txt

Opening 001.txt
Opening 002.txt
Opening 002.txt
        processed 002.txt
Opening 003.txt
[download]

L*

> note that perl -n and perl -p both skip empty files!

They don't, but that part of code is not exposed to us to insert our own code into. Or is it?

#!/usr/bin/perl -n
use warnings;
use strict;

{   package File::ShowName;
    use Tie::Scalar;
    use parent -norequire => 'Tie::StdScalar';
    sub FETCH { print STDERR "Opening ${ $_[0] }.\n"; ${ $_[0] } }
}

BEGIN { tie $ARGV, 'File::ShowName' }

print;
[download]

map{substr$_->[0],$_->[1]||0,1}[\*||{},3],[[]],[ref qr-1,-,-1],[{}],[sub{}^*ARGV,3]

perl -we 'rename $_, "image" . $counter++ . ".jpg" for @ARGV' *
[download]