There is no problem in adding a ng-model because that will help you to use its value. For example:

<select class=account-filter ng-change=customerSelected() ng-model=selectedCustomer>

      <option ng-repeat=account in getCustomerName() track by $index

          ng-class=(account | limitTo: 18)

          ng-bind=account.split('|')[0]

          value={{account}}></option>

</select>

Now you can read the selected customer's value in your controller by simply $scope.selectedCustomer.

Update

After updating the question with more description, you have two option:

Option 1 (recommended)

You can write like this (although, you can achieve much of it in the HTML itself but it is cleaner to do in the controller):

$scope.customerSelected = function() {

     var selectedCustomer = $scope.selectedCustomer;

     if (!selectedCustomer) {

          alert(Please select a customer);

          return;

     }



     var secondId = selectedCustomer.split('|')[2];

     // You can directly put your main logic here but since you want to

     // call a separate method with passing the id

     $scope.doSomethingWithCustomer(secondId);

};



$scope.doSomethingWithCustomer = function(id) {

    // Your main logic here after selecting the customer

};

and modify your HTML as I described above:

<select class=account-filter ng-change=customerSelected() ng-model=selectedCustomer>

      <option ng-repeat=account in getCustomerName() track by $index

          ng-class=(account | limitTo: 18)

          ng-bind=account.split('|')[0]

          value={{account}}></option>

</select>

Option 2 (less cleaner)

$scope.doSomethingWithCustomer = function(id) {

    // Your main logic here after selecting the 2nd customer

};

and modify your HTML as:

<select class=account-filter ng-model=selectedCustomer

    ng-change=doSomethingWithCustomer(selectedCustomer.split('|')[2])>

      <option ng-repeat=account in getCustomerName() track by $index ng-class=(account | limitTo: 18) ng-bind=account.split('|')[0] value={{account}}></option>

</select>

Option 3

If you want to achieve it without the ng-model and without jQuery then you can use a directive:

See a working example below.

var a = angular.module(sa, [])



a.controller(foobar, function($scope) {

  $scope.getCustomerName = function() {

    return ['Foo', 'Bar'];

  };



  $scope.customerSelected = function() {

    console.log(I'm changed);

    alert(I'm changed);

  };

});



a.directive(changeMe, function() {

  return {

    scope: {

      changeMe: '&'

    },

    link: function($scope, element, attr) {

      element.on(change, function() {

           $scope.changeMe();

      })

    }

  }

});

<script src=https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js></script>



<div ng-app=sa ng-controller=foobar>

  <select class=account-filter change-me=customerSelected()>

    <option ng-repeat=account in getCustomerName() track by $index ng-class=(account | limitTo: 18) ng-bind=account.split('|')[0]></option>

  </select>

</div>