Hi
For Activity tracking and various other features and services on Apple Watch and iPhone to work as intended by Apple, you should not share an Apple ID.
Each user should instead have a separate Apple ID and be signed in accordingly on their iPhone and Apple Watch.
Should you wish to share eligible past and future purchases (iTunes music, apps, books, etc), then you can still do so via Family Sharing (a free Apple service). Other features of Family Sharing include a shared family calendar, shared photo album and the ability to set reminders that will alert all family group members:
The following articles provide instructions for:
Creating a new Apple ID:
How to use that new Apple ID on an iPhone:
The person who sets up a new Apple ID should also first unpair their Apple Watch from their iPhone and then pair it again after the iPhone has been configured to use the new Apple ID:
Once you are set up with your own respective Apple IDs on your devices, you can also share Activity results with each other: