How to bind data in json to li using Angular js

Question 1

Why it's not working?

you cannot just attach a variable to the scope when it's value is waiting for on asynchronous call.
when you use 3rd-party libraries that changes the scope you must call $scope.$apply() explicitly

prefer $http over $.ajax and use promises!

DemoApp.factory('SimpleFactory', function ($http) {
  return {
    getCustomer: function(){          
      return $http.post('Home.aspx/getname',{ name: "" });
    })
  }
}

DemoApp.controller('SimpleController', function ($scope, SimpleFactory) {
    SimpleFactory.getCustomer().then(function(customer){
      $scope.Customer = customer;
    },function(error){
      // error handling
    });
});

If you still want to use $.ajax

you must explicitly call $scope.$apply() after the response
you must use promises or callbacks to bind to scope variables.

If you want to first fetch data from the server and than load the view

@Misko Hevery has a great answer: Delaying AngularJS route change until model loaded to prevent flicker

It's not related to your problem but load jquery before you load angular.js

<script src="http://code.jquery.com/jquery-1.10.1.min.js"></script>
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.7/angular.min.js"></script>

Question 2

Your problem is the js (the function "SimpleFactory.getCustomer()") is returning before AJAX call returning..

Also, you should use $http in Angular instead of jquery's ajax, because:

$http returns a "promise" similar to other areas in angular, which means .success, .done are consistent with angular.
$http set the content type to 'application/json' for you on POST requests.
$http success and error callbacks will execute inside of angular context so you don't need to manually trigger a digest cycle - if you use jQuery, then it might be necessary to call $apply..

Like this:

var DemoApp = angular.module('DemoApp', []);

DemoApp.factory('SimpleFactory', ['$http', function ($http) {
    var factory = {};

    factory.getCustomer = function () {
        var promise = $http.post('Home.aspx/getname', {name: ''});
        promise.catch(function(error) {
            alert(error);
        });            

        return promise;
    };

    return factory;
}]);

DemoApp.controller('SimpleController', ['$scope', 'SimpleFactory', function ($scope, SimpleFactory) {
    SimpleFactory.getCustomer().then(function(customer) {
        $scope.Customer = customer;
    });    
}]);

Question 3

Factories in AngularJS are singletons. So the way you've written the code will execute the ajax call when the factory is injected into the controller. You don't see the customer data because the server response will be handled after you assign the json data to the scope variable.

A quick (and dirty) fix which will probably work is wrapping the customer object:

DemoApp.factory('SimpleFactory', function ($rootScope) {
  // ...
  var customer = {};
  // ...

  $.ajax({ 
    // ...
    success: function(data) {
      $rootScope.$apply(function() {
        customer.data = data;
      });
    }
    // ...
  });
});

// In view

<li data-ng-repeat="customer in Customer.data"> <!-- ... --> </li>

A better approach would be to use either to use the builtin $http or the $resource angular service. The last one requires you to make use of RESTful services (recommended). If for any reason you still want to make use of jQuery ajax calls you need some form of telling Angular that the ajax call has been completed: have a look at the $q promise service.