How can I change my nickname in Family Sharing?

I recently got an ipad and set it up with my existing apple id that I have had for 15 years. When I went to add family members with Family share, it identifies me with an old and inappropriate nickname. I want to change this nickname but cannot find any way to do it. I have tried opening itunes and choosing settings but there is no nickname option as suggested in other forums here. I've also logged into my Apple account and tried there. I need to get this nickname that I don't even remember creating changed. How can I do that?

[Re-Titled by Moderator]