Hi
Yes, you can.
There are two different versions of Apple Watch Series 3:
Apple Watch Series 3 (GPS + Cellular)
In respect of the built-in cellular feature, Apple Watch Series 3 (GPS + Cellular) does not lock to any specific carrier and has an embedded SIM / eSIM, which copies information from the SIM card in the paired iPhone when the cellular feature is enabled.
Enabling the built-in cellular feature requires a carrier plan for your iPhone that specifically includes support for Apple Watch Series 3 (GPS + Cellular), including the carrier activating the device on the plan:
Apple Watch - Carriers - Apple
Even if your Apple Watch and iPhone have previously been set up using a plan from one carrier, but you wish to change to another, then you can still do so by following the instructions here, under "Changing carriers":
Set up and use cellular on Apple Watch Series 3 (GPS + Cellular) - Apple Support
Apple Watch Series 3 (GPS + Cellular) can also be used without enabling the built-in cellular feature, in which case it functions like a GPS-only model and can be used in conjunction with a service plan for iPhone from any carrier, with no need to activate the watch on the plan.
Apple Watch Series 3 (GPS)
Apple Watch Series 3 (GPS) models do not have built-in cellular capabilities.
Any data consumed by Apple Watch Series 3 (GPS) is consumed either via the paired iPhone (including Wi-Fi and cellular data) or via a direct connection between the watch and a compatible Wi-Fi network (when the watch cannot connect to the paired iPhone via Bluetooth).
A separate cellular plan for the Apple Watch is not required.