This article explains how to receive text messages on a Samsung Galaxy Watch. It also explains what to do if you're not receiving text messages on your watch.
Text on your Galaxy Watch with the Messages app | Samsung NL
Before you can receive text messages on your Samsung Galaxy Watch, you'll need to enable the feature. Your watch can receive notifications from many different sources, and you can choose whether or not to receive those notifications on a per-app basis. For example, you can choose to receive text message, email, and alarm notifications, but disable everything else.
Here's how to make sure you receive text messages on your Samsung Galaxy Watch:
Open the Galaxy Wearable or Galaxy Watch app on your phone.