Each device needs a unique phone number, it is how they are "addressed" by the phone company. The only way you could do something like that would be to port your existing number to Google Voice then have GV ring both the phone and the watch when someone calls you. Calling out and having your existing number show to the recipient is another story, I know it can be done on the phone but the watch would be another story. Also, not every smartwatch has that capability, which one do you have?
I'll be honest, I don't understand the fascination with having that capability on a watch. My Huawei Watch has speakerphone capability and I never use it, I prefer using a headset. Any time I'd be in a situation where I'd like the watch to have mobile data, I'm not even wearing it as I don't wear it when I go out exercising.