The Apple Watch Series 3 and newer may connect directly to a wireless network- However, in order to do so, it will need to be registered as a separate device. (Note: Apple Watches that only connect to a paired iPhone do not need to be registered.) To locate the hardware address for your Apple Watch you will need to open the Apple Watch app on an iPhone:
1. Open the Watch app.
2. Go to General > About
3. Scroll down to find the "Wi-Fi" Address
4. Once you have completed these steps, you can register the Apple Watch to the network by following the steps for Connecting a device that does not have a web browser.
You will know that your watch is connected to the network if the wifi logo lights up on the watch.