You can store your file2 names and ids in a hash, then loop through file1 and make substitutions:

use warnings;
use strict;

my $f1 = '1.txt'; # set up files 1 through 3
my $f2 = '2.txt';
my $f3 = '3.txt'; 

my %ids;
my $fh;
open $fh, '<', $f2 or die;
while (<$fh>) {
    chomp;
    my ($name, $id) = split /_/;
    $ids{$name} = $id;
}
close $fh;

open my $fho, '>', $f3 or die;
open $fh, '<', $f1 or die;
while (<$fh>) {
    for my $name (keys %ids) {
        s/$name/${name}_$ids{$name}/;
    }
    print $fho $_;
}
close $fh;
close $fho;
[download]