Here is another plugin that makes it easy to handle SMS and push notifications on your website. WordPress Notificator for WooCommerce supports SMS, WhatsApp, and Pushbullet notifications. You can use it to send all kinds of notifications to your customers to keep them in the know. It lets you use different gateways for different countries.
This plugin can be used for admins, customers, and vendors. You can use it to send order changes and stock alert notifications to your customers. It supports TeleSign, Twilio, Nexmo, and other SMS gateways. firassaidi is the developer behind this plugin.