Apple Watch without phone

No.

FYI: Watch is an iPhone accessory.

It's not meant to be used without a paired iPhone.

Watch GPS + Cellular models can make/receive calls, send/receive messages without the iPhone nearby

Provided your carrier has number sharing enabled.

Watch GPS only models can also make/receive calls, send/receive messages but iPhone must be nearby.

All models of Watch (GPS+Cellular/GPS only) must be paired with an iPhone.

No it doesn't need a phone number,I use an iphone 8 without a simcard and my watch works perfectly,it does need a phone though to set it up and communicate and record all your fitness data.I just use an iphone as an accessory to the watch.