• You can retrieve the name attribute directly, no need to search for the first attribute.
• You need the attribute object in order to be able to remove the attribute, anyway.
• Use the getValue method to retrieve the value of the attribute.
• Minor: "reader" sounds like a XML::LibXML::Reader instance, not a normal DOM object.

#!/usr/bin/perl
use warnings;
use strict;

use XML::LibXML;

my $xml = '<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Tr
+ansform">
<xsl:element name="foo">
<xsl:value-of select="bar"/>
</xsl:element>
</xsl:stylesheet>';

my $dom = 'XML::LibXML'->load_xml(string => $xml) or die;
my $xpc = 'XML::LibXML::XPathContext'->new($dom);

for my $element ($xpc->findnodes('//xsl:element')) {
    my ($name_attr) = $xpc->findnodes('@name', $element);
    $element->removeAttribute('name');
    $element->setNodeName($name_attr->getValue);
}
print $dom;
[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]

This is close. The output is:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" versi
+on="1.0">
<xsl:foo>
<xsl:value-of select="bar"/>
</xsl:foo>
</xsl:stylesheet>
[download]

but what I was asking for was:

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" versi
+on="1.0">
<foo>
<xsl:value-of select="bar"/>
</foo>
</xsl:stylesheet>
[download]

Everything you have done so far is great, thank you. If you can help me with this last piece, it will be perfect. I'm sorry for my ignorance. I have a lot to learn when it comes to Perl.

I remember doing battle with XML::LibXML in a similar situation a few years ago. IIRC, what I found back then is that the problem is namespaces - note how the document originally has only one namespace (http://www.w3.org/1999/XSL/Transform) with only one namespace prefix (xsl). What you're asking to do is move the node into a completely different namespace, specifically in this case the default one. I remember not being able to find the appropriate combinations of API calls to achieve this so that the resulting XML looked clean, and playing around by adding $element->setNamespace(...); to choroba's code seems to confirm this, the best I can do so far is <foo xmlns="...">. It seemed that once a node has been created in a namespace, it's stuck there you can't get it back into the default namespace cleanly. Back then I ended up writing a routine to create a new node in the new namespace. Now since this was a while ago, it's possible I missed the appropriate API function, but even now going through the XML::LibXML docs and Googling a bit I still don't see an obvious way.

<update2> Caveat: The below will completely ignore any other attributes in the element being replaced, so for example if you've got <xsl:element namespace=... or use-attribute-sets, that will be ignored and lost! </update2>

Here's what my workaround would look like (based in part on choroba's code):

use warnings;
use strict;
use XML::LibXML;

my $xml = <<'END_XML';
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0" xmlns:xsl="http://www.w3.org/1999/XSL/Tr
+ansform">
<xsl:element name="foo">
<xsl:value-of select="bar"/>
</xsl:element>
</xsl:stylesheet>
END_XML

my $doc = XML::LibXML->load_xml(string => $xml) or die;
my $xpc = XML::LibXML::XPathContext->new($doc);
for my $el ($xpc->findnodes('//xsl:element')) {
    my $newel = $doc->createElement($el->getAttribute('name'));
    $newel->appendChild($_) for $el->childNodes;
    $el->replaceNode($newel);
}
print $doc;

__END__

<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet xmlns:xsl="http://www.w3.org/1999/XSL/Transform" versi
+on="1.0">
<foo>
<xsl:value-of select="bar"/>
</foo>
</xsl:stylesheet>
[download]

Update: Made description more accurate.