.post()takes a string as the second argument, so you can concatenate a custom string using +followed by your string.
var thename = jQuery("input#name").val();
jQuery.post(the_ajax_script.ajaxurl, jQuery("#theForm").serialize() + "&foo=bar",
function(response_from_the_action_function){
jQuery("#response_area").html(response_from_the_action_function);
});
Be careful; the string must be correctly formatted as a url, so you need pairs key=valueseparated by &s.
+ "&foo=bar. & , .serialize(), foo= - , bar - .
, - :
&foo=bar&baz=zip