Is it possible to set up two Apple Watches on the same phone?

Hello, YES. On your iPhone go to Watch app. You will see above your name of your current watch it says "All Watches". Click that. It will show your current paired watch. Below that you will see Add Watch. You can set up one for yourself or for a family member who does not have an iPhone.

In addition to what GeeZ06 said, just as an FYI, be aware that you can only use one watch at a time unless you are setting up a watch for a Family Member.

Set up Apple Watch for a family member - Apple Support

javaliga, Thanks for adding that important point.🤠