Hello Tatebiz,
Congratulations on your new Apple Watch! We’d like to help and get those messages sending and receiving on your watch as expected.
Take a look at If you can’t send or receive messages on your Apple Watch. It has some steps for you to try.
If none of those steps work, try testing the cellular connection on your watch. To do this, put your iPhone in Airplane mode, or disable Bluetooth from Settings > Bluetooth (toggling Bluetooth in Control Center will not work), then disable Wi-Fi from the Apple Watch Control Center (or leaving a Wi-Fi network's coverage). It may take up to 60 seconds for the Watch to establish a cellular connection.
If your Watch successfully shows a green cellular icon in the Watch Control Center, along with signal 'dots', cellular connectivity is working as intended. You may want to contact Apple Support.
Take care!