How can I change the distance measurement on my Apple Watch?

I don't think you can manually set that, though I may have missed something. Here's what Apple says about calibrating your Watch:

Calibrate your Apple Watch for improved Workout and Activity accuracy - Apple Support

Regards.

if you Check the Watch app on your iPhone:

- My Watch > General > Language & Region > Region format

You can also check on your iPhone under:

- Settings > General > Language & Region > Region formats

Units can also be changed in the Health app on your iPhone - for example, via:

- Health Data > Fitness > Walking + Running Distance > Unit

Units used within the fitness apps can also be changed directly on your watch, for example:

- On your watch, open the Workout app and select to start an Outdoor Run.

- When the goal screen is displayed, swipe left / right to the distance goal. Force press on this screen, then choose kilometres (if miles is originally shown).

- Exit from the Workout app (go back one screen by pressing cancel, then press the Digital Crown).

- The Activity app will now show km (and km will also be used for future workouts in the Workout app).

if your Apple Watch isn't connected to a phone please say so