The chime is usually an indication your Apple Watch has detected the connection of the external charger. That suggests there might be a problem with your mains power adaptor and charging cable (magnetic puck) and it is certainly the first place I would check.
I suggest set your watch to charge earlier in the evening so you can observe what happens away from your bedside setup. You *should* see the watch charge to 100% then simply stop active charging and wait quietly on the charger, using external power to supply the watch. The only indication for this should be a single notification on the paired iPhone for completed charging. If the charger power is interrupted then restored it will chime when the power comes back. You can simulate this by disconnecting mains power to the adaptor, or unplugging the charging puck from the adaptor - then put it back to normal. However, it should not happen unless you touch something!
If there is a hardware defect like a problem cable in the charging accessories I would expect the problem to show during charging, not only after the watch reaches 100%.
The other possible checks - try with a different charging cable and magnetic puck if you have one. Try a different mains adaptor. Try a different wall socket. if the problem persists after all these have been checked and tested by substituting known good items, you might have a defect in your Apple Watch. This is unlikely, but if you suspect it is still a contender please contact Apple Support and arrange to get the watch examined and tested.