Apple Watch Family Plan is the only way for the Apple Watch to have a different phone number from the iPhone it is paired to.
NOTE: Some carriers give the Apple Watch an account number which is a phone number, as just about all cellular carriers use your phone number as the account number. Some carriers actually let you dial that number, some do not. But the Apple Watch will still ring when the iPhone's number is called, and SMS/MMS messages are sent to the iPhone they will also be available on the Apple Watch.
Set up Apple Watch for a family member - Apple Support
Set up Apple Watch For Your Kids - Apple Support
Some limitations: Cannot receive SMS/MMS messages, as that depends on a fully paired iPhone. Messaging is pretty much limited to Apple's Messages, unless the messaging service provides an Apple Watch app. Alarms, alerts, notifications on the iPhone are not sent to the Apple Watch. Apple Pay via a credit card is not available. Also not available: Medications, respiratory rate, irregular heart rhythm notifications, ECG, AFib History, Cycle Tracking, Sleep, Wrist Temperature, Blood Oxygen, Walking Steadiness, Audiobooks, Camera Remote, News, Shortcuts, and the double tap gesture.