sflitman,
I finally have a solution I am happy with. It only loops 206 times as that's how many possible 3x3 magic squares using 1-26 there are. Of course, I spent far more of my time (not to mention tilly and tye) figuring out how to get this solution then it would have taken just to let a naive brute force run. Enjoy. This should scale something close to O(N) where N is the number of names that you want to check.

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

my @possible;
for my $x (5 .. 22) {
    for my $y (grep {$_ != $x} 1 .. int((25 - $x) / 2)) {
        my $max = 26 - $x - 2 * $y;
        my $min = $x - 2 * $y - 1;
        for my $z (grep {$_ != $x && $_ != $y} 1 .. ($min < $max ? $mi
+n : $max)) {
            my @square = (
                ($x + $y),          ($x + $z),  ($x - $y - $z),
                ($x - 2 * $y - $z),   ($x),     ($x + 2 * $y + $z),
                ($x + $y + $z),     ($x - $z),  ($x - $y) 
            );
            push @possible, join '', map chr($_ + 64), @square;
        }
    }
}
NAME:
for (qw/PAUL JOHN MARTY SHEILA SMACK SUZY ELSA/) {
    for my $square (@possible) {  
        my $name = $_;
        $name =~ s/[$square]//g;
        if (! length($name)) {
            print "$_ is contained within $square\n";
            next NAME;
        }        
    }
    print "No solution for $_\n";
}
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