if you set it up on your phone, they might be getting a lot more than just your number showing up, there's a chance all calls, texts, and possibly emails, will be going to the watch. Also any notifications that come in when your phone screen is off, will probably go to their watch also.
to set up as a family watch, the person has to be in your "apple family" and the watch MUST have cellular to be set up as a family watch
Family Setup lets family members who don't have their own iPhone enjoy the features and benefits of an Apple Watch.
support.apple.com