Filter will remove an element when the function returns false. So you want it to return false when you encounter an element with name="name" and when it is empty.
var objects = $(".validated").filter(function(){
// Will return false when name="name"
return $(this).attr("name") != 'name';
}).filter(function (){
// Will return false when the value is blank
// Added trim to ensure that blank spaces
// are interpreted as a blank value
return $.trim($(this).val()) != '';
});
A shortened version would be:
var objects = $(".validated").filter(function(){
// Will return false when name="name" or blank value
return $(this).attr("name") != 'name' && $.trim($(this).val()) != '';
});