You have, /^$number/ but you never assign it. But more important, you match on ^-, and then change found back to 0 after printing a line, which so happens to be the first. Might i suggest..

my $found=undef;
while (<FILE>){
 if ($found eq $number and /^-/) 
 {
     print COPYFILE "$_\n";
 }
 elsif (/^($name)/o) 
 {
    $found = $1;
 }
}
close (COPYFILE);
close (FILE);
[download]

Untested, mother aproved. ;)