No receiving text messages on my Apple Watch
What could be the problem?
Apple Watch Series 5, watchOS 6
Message (like notifications) go to either your Apple Watch or iPhone, but not both. If your iPhone is unlocked, you'll get notifications on your iPhone, instead of your Apple Watch. If your iPhone is locked or asleep, you'll get notifications on your Apple Watch, unless your Apple Watch is locked with your passcode. For more info, see:
Notifications on your Apple Watch - Apple Support
(Note: The conversation will still appear on your iPhone regardless.)