I have not tested it

First, you redefine the perl built-in rename. So a call to rename would resolve to CORE::rename(), not the one you just wrote.

Second, you use neither strict nor warnings, which would have indicated:

Not enough arguments for rename at line 22, near "$eachFile)"
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Third, you're using a prototype. Don't. Read When to use Prototypes?, and I quote from a node written by tilly: Prototypes have many silent, nasty and unexpected side-effects..

Last, and most importantly, it does not work (even after correcting the above errors):

use strict;
use warnings;

sub re_name
{
  my $path = $_[0];

  #append a trailing / if it's not there
  if($path !~ /\/$/)
  {
    $path .= '/';
  }

  #loop through the files contained in the directory
  for my $eachFile (glob($path.'*'))
  {

    #if the file is a directory
    if(-d $eachFile)
    {
      #pass the directory to the routine ( recursion )
      re_name($eachFile);
    }
    else
    {
     my @strings = split('/', $eachFile);
     my $fileName = $strings[$#strings];
     my $filePath = '/'.join('/', @strings[2..$#strings-1]);
     system("mv $filePath/$fileName $filePath/newfile");
    }
  }
}
re_name('.');
re_name('/tmp/654653');
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$ mkdir -p /tmp/654653
$ cd /tmp/654653
$ mkdir -p FOO/BAR
$ mkdir -p FOO/TZE
$ touch FOO/BAR/BANANA
$ touch FOO/BAR/APPLE
$ touch FOO/TZE/ORANGE
$ perl 654653.pl
mv: cannot stat `//654653.pl': No such file or directory
mv: cannot stat `/BAR/APPLE': No such file or directory
mv: cannot stat `/BAR/BANANA': No such file or directory
mv: cannot stat `/TZE/ORANGE': No such file or directory
mv: cannot stat `/654653/654653.pl': No such file or directory
mv: cannot stat `/654653/FOO/BAR/APPLE': No such file or directory
mv: cannot stat `/654653/FOO/BAR/BANANA': No such file or directory
mv: cannot stat `/654653/FOO/TZE/ORANGE': No such file or directory
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use strict;
use warnings;
use File::Find;
my $path = '.';
finddepth(\&pattern, $path);

sub pattern {
  print "$_\n";
  rename($_, lc($_));
}

__END__
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