$re = '~.*?(<h2 itemprop="name">\s*<a.*?</h2>\s?|$)~is';
$str = '<Лишний код>
<Лишний код>
<h2 itemprop="name"><a href="https://site.ru/1page.html">Page1</a></h2>
<Лишний код>
<Лишний код>
<Лишний код>
<h2 itemprop="name"><a href="https://site.ru/2page.html">Page2</a></h2>
<Лишний код>
<Лишний код>';
$subst = "$1";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php