# get prefix
sub prefix {
    my @w = length($_[0]) > length($_[1]) ? reverse @_ : @_;
    my $len = 1;
    my $f;
    $len++ while     $w    = substr($w[0],0,$len)
              #  and $w[1] =~ /^$w/ # no m// needed, index is fine
                 and  0   == index( $w[1],$w) 
                 and $len <= length $w[0] 
                 and $f    = $w;
    return if $f eq $w[0];
    $f;
}
   
# get suffix
sub suffix {
    my @w;
    push @w, scalar reverse($_) for @_;
    $ret = reverse prefix(@w);
}   

while(<DATA>) {  # DATA section contains names as per OP's link
    push @list, (split/,/)[0];
}

# get prefixes and suffixes
my (%names, %pre, %suf);

$names{$_}++ for @list; # updated per [id://759430]

while(@list) {
    my $first = $ARGV[0] || shift @list; # updated per [id://759430]
 #  next if $names{$first}++; # store for convenient lookup
    for my $name (@list) {
        my $s = prefix($first,$name);
        ++$pre{$s}->{$first} and ++$pre{$s}->{$name} if $s;
        my $s = suffix($first,$name);
        ++$suf{$s}->{$first} and ++$suf{$s}->{$name} if $s;
    }
    last if $ARGV[0]; # updated per [id://759430]
}   

# get pairings. Concatenate each prefix which each suffix
# and see if it comes to a compliment, er, a complement
# which can be looked up in the %names hash

my @pre = keys %pre;
my @suf = keys %suf;

for my $pre(@pre) {
    for my $suf (@suf) {
        if ($names{$pre.$suf}) {
            print "found: prefix(@{[keys %{$pre{$pre}}]}) = $pre, "
               .  "suffix(@{[keys %{$suf{$suf}}]}) = $suf, " 
               .  "$pre.$suf = $pre$suf\n";
        }
    }
}