How to change airdrop name from name of main person on family plan

I have a family plan with my parents and just got a new phone. I airdropped a pic to someone recently and it came up as my Dad’s name, who’s the main person listed on the family plan. I’ve gone to settings->general->about and the name there is me, but I can’t figure out how to change the name that comes up when I airdrop something.