Also using Fisher-Yates:

use strict;
use warnings;

my ($x, $t);
my @n = map (/\.(.*)/, <DATA>);
for (0..($#n - 1)) {
    $x = int(rand() * ($#n - $_ + 1)) + $_;
    $t = $n[$x]; $n[$x] = $n[$_]; $n[$_] = $t;
}
for ($_ = 0; $_ < $#n; $_ += 2) {
    print "Group ".($_ / 2).": ".$n[$_]." and ".$n[$_+1]." are partner
+s\n";
}

__DATA__
1.bobby
2.jane
3.charleen
4.markus
5.gabriel
6.Alex
[download]