you can't have a different or stand alone number on your watch.
It does have a unique sim, but it does not have a unique number. it's a special part
you don't just "bluetooth your phone to the watch" like a speaker. They are tied together at a basic OS level. You can't even tell time on the watch unless you've paired it to a phone. The 2 devices are always connected. even if you're out with the watch, and you've left the phone at home, they still communicate over the internet using cell or wifi. some notifications are forwarded from your phone, so they may not work unless your phone is turned on and connected. Some things like iMessage will go through without the phone being connected somewhere, since the watch is also singed into your appleID. For me (T-mobile US) the watch will still ring when the phone is turned off. Not sure if that applies to all carriers. Not sure about regular SMS messages.