<select ng-show="isEditMode(todo.id)" id="assignee" name="assignee"
        ng-model="todo.assignee" required
        ng-options="user.name for user in users">
</select>

$scope.todos = Todo.query();
$scope.users = User.query();

[
{
    "id": 157,
    "description": "my description 0",
    "deadline": 1392073200000,
    "assignee": {
        "id": 34,
        "name": "User 1",
        "email": "user1@hotmail.com"
    },
    "comment": "my comment 0",
    "done": true
}
...
]

[
{
    "id": 34,
    "name": "User 1",
    "email": "user1@hotmail.com"
},
{
    "id": 35,
    "name": "User 2",
    "email": "xxc@gmail.com"
},
{
    "id": 36,
    "name": "User 3",
    "email": "xx@hotmail.com"
}
]

<tr ng-repeat="todo in todos | filter:query | filter:{assignee:queryAssignee} | filter:queryDone" ng-class="{danger: isDue(todo)}">
                    <td>

ng-model="todo.assignee"

ng-model="todo.assignee.name"

<select ng-show="isEditMode(todo.id)"
    ng-model="todo.assignee.name" required
    ng-options="user.name as user.name for user in users">
</select>

<select ng-model="todo.assignee" required>
    <option ng-repeat="user in users" value="{{user}}" ng-selected="todo.assignee.name === user.name">
        {{user.name}}
    </option>
</select>

todo.assignee.name = "User 3" // like this

todo.assignee // didn't change the id & email
/* {"id": 34,
    "name": "User 1",
    "email": "user1@hotmail.com"} */

When you select one of option, it assign object value to model todo.assignee, so let what you want.

todo.assignee.name = {
    "id": 36,
    "name": "User 3",
    "email": "user3@hotmail.com"
} // like this

todo.assignee // now change the whole value
/* {"id": 36,
    "name": "User 3",
    "email": "user3@hotmail.com"} */

<select ng-show="isEditMode(todo.id)" id="assignee" name="assignee"
        ng-model="todo.assignee" required
        ng-options="user as user.name for user in users track by user.id">
</select>