Text messages
My text messages on my apple watch for some reason will only send SMS and not iMessage. At first it would but now it stopped after 2 weeks of ownership. I have the Apple watch 4 with cellular.
Apple Watch Series 4, watchOS 5
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Go to Settings → Messages → Send & Receive and make sure that 'Start new conversations' is set to your phone number, not e-mail. Just reset the Watch holding down both side buttons until the Apple Logo appears. In my case the messages were not getting sent in iMessage, just as SMS.