Having done this last night, the best process is;
1. Open Watch app > General > About > Name [Give your current AW a unique/identifiable name]
2. Perform a backup on the iPhone of which the old AW is connected to. (The AW is backed up through iPhone backup)
3. Open Watch app > All Watches > Add Watch
4. Follow the prompts/instructions to add your new AW until installed
5. Watch app > All Watches > Identify OLD AW from unique name given at start > Tap the circled ! > Unpair Apple Watch
6. iPhone > Settings > [your name] > If your old AW is displayed, tap on it and ‘Remove from account’
7. Enjoy your new watch!