<?xml version="1.0" encoding="UTF-8"?>
<web-app id="WebApp_ID" version="2.4" xmlns="http://java.sun.com/xml/n
+s/j2ee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:sch
+emaLocation="http://java.sun.com/xml/ns/j2ee http://java.sun.com/xml/
+ns/j2ee/web-app_2_4.xsd">
    <display-name>SOMEGUY</display-name>
    <servlet>
        <display-name>
        Apache-Axis Servlet</display-name>
        <servlet-name>AxisServlet</servlet-name>
        <servlet-class>
        org.apache.axis.transport.http.AxisServlet</servlet-class>
    </servlet>
    <servlet>
        <display-name>
        Axis Admin Servlet</display-name>
        <servlet-name>AdminServlet</servlet-name>
        <servlet-class>
        org.apache.axis.transport.http.AdminServlet</servlet-class>
        <load-on-startup>100</load-on-startup>
    </servlet>
    <servlet-mapping>
        <servlet-name>AxisServlet</servlet-name>
        <url-pattern>/servlet/AxisServlet</url-pattern>
    </servlet-mapping>
    <servlet-mapping>
        <servlet-name>AxisServlet</servlet-name>
        <url-pattern>*.jws</url-pattern>
    </servlet-mapping>
    <servlet-mapping>
        <servlet-name>AxisServlet</servlet-name>
        <url-pattern>/services/*</url-pattern>
    </servlet-mapping>
    <servlet-mapping>
        <servlet-name>AdminServlet</servlet-name>
        <url-pattern>/servlet/AdminServlet</url-pattern>
    </servlet-mapping>
    <welcome-file-list>
        <welcome-file>index.html</welcome-file>
        <welcome-file>index.htm</welcome-file>
        <welcome-file>index.jsp</welcome-file>
        <welcome-file>default.html</welcome-file>
        <welcome-file>default.htm</welcome-file>
        <welcome-file>default.jsp</welcome-file>
    </welcome-file-list>
</web-app>
[download]

When I run your code, it generates two outputs:
• some to STDOUT
• other to file web_bu.xml
My guess is that you want all output to go to the file and none to STDOUT. Is that correct? So, what you just posted should be the contents of the output file?

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

my $out_file = 'C:\web_bu.xml';

my $t = XML::Twig->new(
    twig_handlers   => {'display-name' => \&convert},
    pretty_print    => 'indented'
);

$t->parse(*DATA);
open (my $fh_out, '>', $out_file) or die "unable to open '$out_file' f
+or writing: $!";
$t->print($fh_out); # this prints to the filehandle

sub convert {
    my ($t, $elt) = @_;
    my $txt = $elt->text();
    if ($txt =~ /wtw_reports/i) {
        $elt->set_text('SOMEGUY');
    }
}
[download]

That's correct - I want to write all of the contents of the original file to an XML file, replacing the value inside the first <display-name>.