There is no built-in method/function to "rename" an attribute in javascript, but you can create new attributes and remove other ones...
$('a.testingCase[title]').each(function() {
var $t = $(this);
$t.attr({
newTitleName: $t.attr('title')
})
.removeAttr('title');
});
Blabla
Bloo
Edit: added in the bit that makes it only select a elements with class="testingCase"