foreach my $name (@$fields) {
  # ...
  my $namedisplay = $1 if($name =~ /AS\s+(\S+)/i);

  warn "namedisplay: $namedisplay"; # 1-st warn

  # that's the lines I added to the code:
  if ( !$namedisplay
       && exists($obj->{labels}->{$name})
       && $obj->{labels}->{$name})
  {
    $namedisplay = $obj->{labels}->{$name};
  }
  warn "namedisplay: $namedisplay"; # 2-nd warn

  # ...
}

##</code><code>##

my $namedisplay;
$namedisplay = $1 if($name =~ /AS\s+(\S+)/i);