Here are some functions that will do this, but more important maybe, a harness that will let you try your own:

#!/usr/bin/perl -w
use strict; 

use Test::More qw(no_plan);

my @data             = read_data();
my @expected_results = read_data();

foreach my $name qw(cut_join_split cut_regexp cut_substr)
  { no strict 'refs';
    my $func= \&$name;
    my @results= map { $func->($_) } @data;
    ok( eq_array(\@results, \@expected_results), $name)
      or diag( "expected: " . join( ' - ', @expected_results) . "\n",
               "got     : " . join( ' - ', @results) . "\n");
  }
   


sub cut_join_split
  { my $filename= shift;
    return join( '_', (split /_/, $filename)[0..1]);
  }

sub cut_regexp
  { my $filename= shift;
    return $filename=~ m{^([^_]*_[^_]*)};
  }

sub cut_substr
  { my $filename= shift;
    my( $index, $sep, $sep_number)= ( 0, '_', 2); # to find _ number 2
    foreach (1..$sep_number)
      { $index = index( $filename, $sep, $index+1); }
    return substr( $filename, 0, $index);
  }


sub read_data
  { local $/="\n\n"; return grep {$_} map { s{#.*}{}; chomp; $_ } spli
+t( "\n", <DATA>); }


__DATA__
# data
smith_13_503_de7.p
smith_13_502_de7.v
jones_104_503_de7.p
jones_104_502_de7.v
# you might want to add more filenames to your test set

# expected results
smith_13
smith_13
jones_104
jones_104
[download]