My custom ringtone and notification sound was not working. I fixed it by restarting the watch, and going to the Galaxy app and listening to all the default sounds until I heard mine. It seems users are reporting a random default sound becoming the custom one.
If you do not have the custom sound on your watch, you can use this link to be able to help you get the sound on your watch. Selecting the ringtone will have to be on your phone through the app, but this works.