To detect that concatenation of data is taking place, you can keep track of whether the last function call was to the data processing function.
e.g. using $this->inside_data variable below:

<?php
xml_set_element_handler($this->parser, "start_tag", "end_tag");
xml_set_character_data_handler($this->parser, "contents");

protected function contents($parser, $data)
{
    switch ($this->current_tag) {
            case "name":
                if ($this->inside_data)
                    $this->name .= $data; // need to concatenate data
                else
                    $this->name = $data;
                break;
         ...
    }
    $this->inside_data = true;
}

protected function start_tag($parser, $name)
{
    $this->current_tag = $name;
    $this->inside_data = false;
}
        
protected function end_tag() {
    $this->current_tag = '';
    $this->inside_data = false;
}
?>