Under iphone settings, Apple ID is correct but has wrong name attached

Hello, I have a family plan. I set up a phone for the other member but it became overlapped, in some way with his identity and not mine. I don't know what I did to create this quirk but I can't seem to fix it. In one case that I can duplicate, on my iphone, under settings, I click on my name/apple id/icloud/logo at the top of the list. At that point, my info seems correct. My name is there as well as my email address. But, when I press on the logo image again, it comes up with the name of my family member instead. Don't know where to go with this. Please direct me and, Please, give me all the steps required. Thanks in advance. Included are images of the steps I took. They show my iphone screen in settings after I click on my Name/logo. Then, the other image shows what comes up when I click on my logo again. It has the name of my family member.