Apple Watch, series 4 (gps & cellular)

You MUST own an iPhone to setup the Apple Watch, and to provide software updates, get Apple Watch apps, send/receive SMS/MMS texts. Also the cellular model shares the iPhone's phone number, so you need an iPhone for that as well.

But the cellular Apple Watch can leave the iPhone home while you go for a run, bike ride, hike etc... But you should leave the iPhone powered up and connected to the network, as the Apple Watch will still "Phone Home" for some services, such as SMS/MMS texing. iMessage texts do not need the iPhone, but the cellular radio used in the Apple Watch does not do SMS/MMS, hence the need to relay via the iPhone if it can find it on the internet.

No Watches do not have its own number, it's shared the same number as the iPhone.