Try using a custom filter before the search filter like this:
Plunkr
index.html
<body ng-controller="DemoCtrl">
<p>Selected: {{country.selected}}</p>
<ui-select ng-model="country.selected" theme="selectize" style="width: 300px;">
<ui-select-match placeholder="Select or search a country in the list...">{{$select.selected.name}}</ui-select-match>
<ui-select-choices repeat="country in countries| removeBlanks | filter: $select.search ">
<span ng-bind-html="country.name | highlight: $select.search"></span>
</ui-select-choices>
</ui-select>
</body>
app.js
'use strict';
var app = angular.module('demo', ['ngSanitize', 'ui.select']);
app.controller('DemoCtrl', function($scope, $http) {
$scope.country = {};
$scope.countries = [
{name: 'a'},
{name: 'b'},
{notName:'xx'}
];
$scope.ignore = {notName:'xx'};
});
app.filter('removeBlanks', function() {
return function( items) {
var filtered = [];
angular.forEach(items, function(item) {
if(!item.hasOwnProperty('notName')){
filtered.push(item);
}
});
console.log('filtered', filtered);
return filtered;
};
});