In your case it is possible to avoid using regex and use ctype functions.
e.g. as a function:
<?php
function checkName($name) {
$len = strlen($name);
//set the locale to C so only [a-zA-Z] for alpha
setlocale(LC_CTYPE, 'C');
if ($len > 3 && $len < 10 && ctype_alnum($name))
return true;
else
return false;
}
?>