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

my %name = map {chomp; $_ => undef} <DATA>;

my $num_names = 0;
for my $person ( keys %name ) {
    my @names = split " " , $person;
    $num_names = @names if @names > $num_names;
    $_ = ucfirst lc $_ for @names;
    $name{ $person } = \@names;
}
my $finished = 0;

my $index = 0;
while ( ! $finished ) {
    my $update = 0;
    for my $person ( keys %name ) {
        next if ! $name{$person}[$index];
        if ( $name{$person}[$index] =~ /(\w+)\w/ ) {
            my $new_name = $1;
            if ( ! grep { $new_name eq $_ }
                map { $name{$_}[$index] }
                grep { @{$name{$_}} == @{$name{$person}} } keys %name
               ) {
                    $update = 1;
                    $name{$person}[$index] = $new_name;
            }
        }
    }
    $index++ if ! $update;
    $finished = 1 if $index > $num_names;
}
print "$_ => @{ $name{$_} }\n" for keys %name;
[download]

Alan Harper => A H     <-- AMBIGUOUS!
Adam Harper => Ad Ha
[download]

The requirement is that all derived 'initials' should be unambiguous in which name they refer to.

'A H' could refer to Alan or Adam.

My code does this:

Adam Harper => AdHa
Alan Harper => AlHa
[download]

EdwardG,
Ok - I interpreted the requirement differently. Since there are only two possibilities and "Ad Ha" can only refer to 1, "A H" must refer to the other. I believe the following accomplishes what you want - and is actually a bit better than your solution (I think). If I am wrong - I give up.

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

my %data;
my $last = 0;
while ( <DATA> ) {
    chomp;
    my @names = split;
    $last = @names if @names > $last;
    $_ = ucfirst lc $_ for @names;
    $data{ "@names" } = \@names;
}

for my $index ( 0 .. $last ) {
    for my $person ( keys %data ) {
        next if ! $data{$person}[$index];
        my $old_name = $data{$person}[$index];
        for my $length ( 1 .. length $old_name ) {
            $data{$person}[$index] = substr( $old_name, 0, $length );
            my $match = 0;
            for ( keys %data ) {
                next if $_ eq $person || @{$data{$_}} != @{$data{$pers
+on}};
                my $test_name = $data{$_}[$index];
                $data{$_}[$index] = substr( $test_name, 0, $length );
                my ($s_name , $s_test) = ("@{$data{$person}}", "@{$dat
+a{$_}}");
                $data{$_}[$index] = $test_name;
                if ( $s_name eq $s_test ) {
                    $match = 1;
                    last;
                }
            }
            last if ! $match;
        }
    }
}
print "@{ $data{$_} } =>\n" for keys %data;
[download]

The reason why I say my code is a bit better is because:

__DATA__
Victor Mcduffie
Viola Mcnamee

# Yours
Vic Mcd
Vio Mcn

# Mine
V Mcn
V Mcd
[download]

Cheers - L~R