i have a lost apple watch but don't know who it belongs to

Unless the person who lost the watch puts it in Lost Mode and provides his/her contact info on the watch screen, there is no way to contact the owner. Apple will not provide that info you or anyone else. See the "Put your Apple Watch in Lost Mode" section in:

If your Apple Watch is lost or stolen - Apple Support

Turn it over to your local police or the lost and found in the area where you found it.

I would much rather want to be able to email the person the watch belongs to or text them if so privately with a hidden number or not hidden