If you can provide a sample of your data that would help in giving a precise answer (use Data::Dumper; print Dumper($more_data);). In addition, try some things out yourself and post here if you have questions about the code. I think the general concept would be something like this:

while ( my ($key,$name) = get_key_and_name() ) {
  my @data;
  while ( my ($entry) = get_data_for_key($key) ) {
    push @data, { NUMBER => $entry->{NUMBER}, etc=>"etc" };
  }
  my $data_tmpl = HTML::Template->new(filename => 'data.tmpl');
  $data_tmpl->param(NAME => $name, DATA => \@data);
  write_file("/location/$key.html", $data_tmpl->output);
}
[download]

(once again untested and based only on the docs - just trying to show the concept of nested while loops here)

Without knowing what $more_data looks like, I can't say what the placeholders get_key_and_name() and get_data_for_key() should look like.