use strict;
use warnings;
use XML::Twig;

my $xml = q(
<sites>
<site siteid="ONE">
   <name>name1</name>
   <address>address1</address>
   <contact>contact1</contact>
</site>
<site siteid="TWO">
   <name>name2</name>
   <address>address2</address>
   <contact>contact2</contact>
</site>
</sites>
);

my %handlers = ( 'name[string() =~ /name2/]' => sub { my ($twig, $cnt) = @_; $cnt->parent->delete;} );
my $twig= new XML::Twig( PrettyPrint   => 'indented', twig_handlers => \%handlers);

$twig->parse($xml);
print $twig->sprint;