Apple Watch with Cellular connection

I have a silly question, but I'm a first time apple watch user. When I added a cellular plan to my watch, it got a 'new' cell phone number (not the same one as my cell phone). If I leave my cell phone at home and go away and someone rings my cell phone, will that call also ring on my watch over the cellular network? Or do I need to set up call forwarding on the phone for that to work?

Similarly, if I make calls from my watch, when my phone is not around, will people see my usual number or the watch number?

Thank you!