Watch don‘t ask which club was used

Hello, can you check the settings to ensure Club Prompt isn't disabled?

Press Menu button, and select Settings > Golf Settings > Club prompt

Make sure it is toggled green.

yes, it‘s on and green

You also need the tracking enabled (the one above club prompt)

both are enabled

i‘m left handed and wear the watch on my left hand. is it possible that the watch only can detect the swing on my right wrist?

That will be why. You need to tell the watch in general settings that it's on the right hand wrist and Garmin suggest that the leading wrist is better for shot detection.