the concept of the hash I am trying to have is,

A => B, C, D, E
B => A, C, D, E
C => A, B, D, E
D => A, B, C, E
E => A, B, C, D
[download]

It strikes me as a bit wasteful to have so many copies of all the names. And it would be worthwhile to figure out an easy way to initialize the complete structure from the simplest possible listing of name sets. Here's what I would propose:

#!/usr/bin/perl

use strict;
use warnings;

# start with an array of arrays (list of lists, which can come from a 
+data file):
# each row contains all the "synonymous" names in a set, and
# each element in the row becomes a hash key whose value is
#    a reference to the whole row/set of synonymous names:

my %altnames;  # will be a HoA

while (<DATA>) {
    my @nameset = split;
    for my $name ( @nameset ) {
        if ( ! exists( $altnames{$name} )) {
            $altnames{$name} = \@nameset;
        }
        else {
            my $newname = $name;
            $newname .= " " while ( exists( $altnames{$newname} ));
            $altnames{$newname} = \@nameset;
        }
    }
}

for my $name ( qw/Allen Bill Chuck Dave Edward Jan/ ) {
    my $modifier = '';
    for ( grep /^$name\s*$/, keys %altnames ) {
        print "The name $_ is $modifier a member of the set @{$altname
+s{$_}}\n";
        $modifier = 'also';
    }
}

__DATA__
Allen Al
Charles Chuck Chas
David Dave
Edward Eddie Ed
Janet Jan
Janice Jan
William Will Willie Bill Billie
[download]

That plays a little game with the name strings to make sure that you can keep track of different name sets containing the same nickname: just add spaces at the end of a previously seen nickname until it becomes a unique key in the altnames hash. Then when searching the hash, make sure to look for the target name optionally followed by spaces. (If the results are going to a web page, the extra spaces won't affect the display.)

Note that by storing multiple references to the same array in the hash, you are not using extra memory to store copies of the names -- each nameset is stored exactly once.

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