I can't receive sms on my apple watch when my iphone is off

Read the footnotes on the following webpage

https://support.apple.com/en-us/HT205547

SMS/MMS requires the iPhone be powered on and connected to the Internet.

iMessage and similar internet based messaging services do not need the iPhone if they have a proper Apple Watch app.

You need to be connected to WiFi or Cellular for that to happen.

Yes it is you need your phone to be on in order to use your cellular network.