A direct way without explicit shuffle (only half the rand calls):

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

my @people = map /\.(.*)/, <DATA>;
my $group = 1;
while (@people) {
    my $person1 = shift @people;
    my $pos = rand @people;
    my $person2 = $people[$pos];
    $people[$pos] = $people[-1];
    pop @people;
    printf "Group %d: %s and %s\n", $group++, $person1, $person2;
}

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