Q: problems with sending digital message with apple watch

Hi - try these steps, which have worked for others:

After pairing Apple Watch with an iPhone, you may need to wait an hour or more before you can receive a Digital Touch.

• In the Contacts app on your iPhone:
  • Check that the contact card for each friend includes their Apple ID email address and iPhone phone number (edit the contact cards where necessary).
  • Check that your own contact card includes your Apple ID email address and your own iPhone phone number.
• Check that you have added your friends to the Friends list on your Apple Watch:
  • On your iPhone: Apple Watch app > My Watch > Friends.
  • To add more friends: In the Friends list > Add Friend > tap someone in the list of contacts. (If someone isn't in the list, open Contacts on your iPhone, add them there, then try again).
• [You may find that this step is not necessary: Delete old iMessage conversations with your friends - on your iPhone and Apple Watch:
  • iPhone > Messages > swipe left on a message thread > delete.
  • Apple Watch > Messages app (from the Home screen - accessed via single press on the Digital Crown) > swipe left on a message thread > tap on trash.]
• Set new Messages conversations to start from your iPhone's phone number.
  • iPhone > Settings > Messages > Send & Receive > scroll down to Start New Conversations From > choose your iPhone phone number.
• On your iPhone in the Apple Watch app: My Watch > General > Reset > tap on Reset Sync Data (you will not see anything happen after tapping it - the process runs in the background). Wait for a minute or so before continuing.
• Disable and re-enable iMessage on your iPhone:
  • iPhone > Settings > iMessage > toggle off / on again.
• Restart both your iPhone and your Apple Watch.
  • Restart Apple Watch: Press and hold the side button until you see the Power Off slider; Drag the slider to turn off completely; Afterwards, press and hold the side button until you see the Apple logo.
• To send a Digital Touch:
  • Press the side button on your watch > Choose a friend (turn the Digital Crown then tap on the icon or picture in the middle of the display) > Tap the Digital Touch icon (pointed finger).
  • Send a sketch (draw on the screen using your finger), a tap (tap the screen once or more) or your heartbeat (place two fingers on the screen until you see and feel your heartbeat).

More help here: Use Digital Touch - Apple Support