You just want to print the elements of an array. It takes a little digging to get to the array, but you've already done most of that. The only missing bit is casting the array reference to an array. The magic is @{$machine->{file}{filename}}. Here's the result:

use strict;
use warnings;
use XML::Simple;

my $str = <<XML;
<config>
    <server>
        <name>server1</name>
        <file>
            <filename>/etc/named.conf</filename>
            <filename>/etc/nsswitch.conf</filename>
        </file>
    </server>
    <server>
        <name>server2</name>
        <file>
            <filename>/etc/named.conf</filename>
            <filename>/etc/nsswitch.conf</filename>
            <filename>/etc/hosts</filename>
        </file>
    </server>
</config>
XML

my $xml = new XML::Simple (KeyAttr=>[]);
my $data = $xml->XMLin ($str);

foreach my $machine (@{$data->{server}}) {
    my $name = $machine->{name};
    print "$name\n";
    print "\t@{$machine->{file}{filename}}\n";
}
[download]

Prints:

server1
    /etc/named.conf /etc/nsswitch.conf
server2
    /etc/named.conf /etc/nsswitch.conf /etc/hosts
[download]