The typical approach would be to read the data into an array, shuffle it, then just pull off the elements (in this case pairs)

# simulate chomp( my @people = <FILE> );
my @people = qw( bobby jane charlen markus gabriel alex );
fisher_yates_shuffle(\@people);
printf "Pair %s %s\n", shift(@people),shift(@people) while @people;

sub fisher_yates_shuffle {
    my $array = shift;
    for (my $i = @$array; --$i; ) {
        my $j = int rand ($i+1);
        next if $i == $j;
        @$array[$i,$j] = @$array[$j,$i];
    }
}
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