Instead of .val() use .text(), like this:
$(".ui-datepicker-month").live("click", function () {
var monthname = $(this).text();
alert(monthname);
});
Or in jQuery 1.7+ use on() as live is deprecated:
$(document).on('click', '.ui-datepicker-month', function () {
var monthname = $(this).text();
alert(monthname);
});
.val() is for input type elements (including textareas and dropdowns), since you’re dealing with an element with text content, use .text() here.