Can I hook a TMobile watch to Verizon if I change services

Changing carriers

On your iPhone, open the Apple Watch app. Tap the My Watch tab, then tap Cellular. Your Apple Watch should automatically switch to the carrier that your iPhone is using. If you need to add a new plan, tap Add a New Plan, then follow the onscreen steps.

Set up cellular on your Apple Watch - Apple Support

In theory, yes, but Verizon has had problems changing from another carrier with the watch.