有没有办法用PHP / AJAX返回更多文本？

I'm trying to change the style of '$.notify' within my AJAX code from my PHP form processing code. I need it to return 'success' or 'error'.

Here's an example of my AJAX code:

    $(function() {
        $("#name-submit").submit(function(event) {
            event.preventDefault();
            if ($("#name").val() != "") {
                $.ajax({
                    method: "POST",
                    url: "<?=updateNameFile?>",
                    data: {
                        name: $("#name").val()
                    }
                }).done(function(msg) {
                    $.notify(msg, "success");
                });
            } else {
                $.notify("<?php echo $language_form_message_invalid_data; ?>", "error");
            }
        });
    });

Here's an example of my PHP code:

    public function updateName($name, $id){
        $pdo = $this->pdo;

        if(isset($name) && isset($i)){
            $stmt = $pdo->prepare('UPDATE users SET name = ? WHERE id = ?');

            if($stmt->execute([$name, $id])){
                $_SESSION['user']['name'] = $name;
                session_regenerate_id();
                return true;
            } else {
                $this->msg = 'An error occurred when changing your name';
                return false;
            }
        } else {
            $this->msg = 'Please provide valid information';
            return false;
        }
    }

Again, I need it to return 'error' or 'success' into my AJAX code to style the notifications correctly.