Using pseudo(hash-based)-bit-vectors, this code is somewhat easier on the eyes (IMHO):

#! perl 
use strict;

my (%name);
while (<DATA>){
    my( $n, $rest ) = split;
    $name{$n}{$_}=1 for ( split ',', $rest );
} 

print "\t",map ({"$_\t"} sort keys %name),"\n"; # First line

for my $n1( sort keys %name){
   print "$n1:\t";
   for my $n2( sort keys %name){
           my $count=scalar keys %{$name{$n2}};
            $name{$n2}{$_} and $count-- for keys %{$name{$n1}};
           print "$count\t";
   }
   print "\n";
}
__DATA__
Name1  USA,Canada,Yemen
Name2  Canada,Portugal,India
Name3  China,HongKong,Canada
Name4  London,Amsterdam,Ireland,USA
Name5  India,USA,Canada
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My results seem transposed because of a different approach to counting.