On the Apple Watch Series 3 Do you have to have a seperate phone number to make and receive calls without your iPhone near by?

Hi

No - Apple Watch Series 3 (GPS + Cellular) uses the same phone number as your iPhone.

There are two different versions of Apple Watch Series 3: GPS models and GPS + Cellular models. The built-in cellular feature is only available on Apple Watch Series 3 (GPS + Cellular) models:

• Apple Watch - Compare - Apple
• Apple Watch Series 3 - Apple

Apple Watch (GPS + Cellular) has a built-in eSIM that copies information from the paired iPhone's SIM card. The built-in cellular features require a carrier service plan that specifically includes support for the watch, including the carrier activating the device on the plan:

Apple Watch - Carriers - Apple

The features - including for making and receiving calls - that are available under various different circumstances are explained here, including in the footnotes:

How to use your Apple Watch without your iPhone nearby - Apple Support

I will have a separate #, but will show up as your regular number through "number sync" (at least thats what AT&T are calling it. Also, if your phone is off or not connected to either internet or wifi you will not be able to send and receive SMS or MMS messages.

The information that I have read is that your Apple Watch with LTE will share the phone number with the iphone it is paired to.

I hope this helps.

Paul