It's a little bit tricky but not impossible :
You need to implement your own view helper and use it with your element.
At first, you must add a custom view helper path :
How to add a view helper directory (zend framework)
Implement your helper :
class View_Helper_CustomSubmit extends Zend_View_Helper_FormSubmit
{
    public function customSubmit($name, $value = null, $attribs = null)
    {
        if( array_key_exists( 'value', $attribs ) ) {
            $value = $attribs['value'];
            unset( $attribs['value'] );
        }
        $info = $this->_getInfo($name, $value, $attribs);
        extract($info); // name, value, attribs, options, listsep, disable, id
        // check if disabled
        $disabled = '';
        if ($disable) {
            $disabled = ' disabled="disabled"';
        }
        if ($id) {
            $id = ' id="' . $this->view->escape($id) . '"';
        }
        // XHTML or HTML end tag?
        $endTag = ' />';
        if (($this->view instanceof Zend_View_Abstract) && !$this->view->doctype()->isXhtml()) {
            $endTag= '>';
        }
        // Render the button.
        $xhtml = '<input type="submit"'
                . ' name="' . $this->view->escape($name) . '"'
                        . $id
                        . ' value="' . $this->view->escape( $value ) . '"'
                                . $disabled
                                . $this->_htmlAttribs($attribs)
                                . $endTag;
        return $xhtml;
    }
}
So, you assign the helper to the element :
$submit = $form->createElement( 'submit', 'submitElementName' );
$submit->setAttrib( 'value', 'my value' );  
$submit->helper = 'customSubmit';
$form->addELement( $submit );
This way, you can retrieve the value of the submitted form :
$form->getValue( 'submitElementName' );