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You have to say "Hey Siri, message [name]"
It works better when you give the command right after saying Hey Siri. That's how I do it and it works most of the time unless I have bad cell coverage
 
Do you wait until the watch screen totally wakes up? You have to delay your "Hey..." Until you see the screen light up.
 
Takes a little practice but Siri works VERY well for me.

There might even be a setting to turn Siri on if you have not checked. Siri is much valued for me on my watch.
 
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