I threw together a solution that is very similar to what Kenosis has suggested. This code creates a %file_info hash. In the code below, the last file name encountered for a given prefix gets stored in the hash. If you want to do other things (like keep track of file type, etc.) then you could modify the %file_info hash. Basically, you want to create a data structure that contains all the information you want to track.

#!/usr/bin/env perl

use strict;
use warnings;

use Path::Tiny;
use File::Find::Rule;

my $dir = shift or die 'No directory given.';
my $dir_path = Path::Tiny->new($dir);

my @files = File::Find::Rule->file()->in( $dir_path );

my %file_info;

foreach my $file (@files) {
    my $file_name = path($file)->basename;
    my $fn_without_ext = $file_name;
    $fn_without_ext =~ s/\..{3}$//;
    $file_info{ path($file)->dirname }{ $fn_without_ext } = path($file
+)->basename; 
} 

foreach my $found_dir (keys(%file_info)) {
    my $file_name = (values %{$file_info{$found_dir}})[0];
    my $file_to_process = path($found_dir, $file_name);
    #process the file here (e.g. use the 'system' command)
    print "Processing this file: $file_to_process\n";
}

exit;
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