Why does my name show up in red in group chat in the Messages app?

I started a group chat with three other people who all have iPhones. It's worked great for the last six months but now suddenly when I post in the group, it does not show up in the group but goes to each person's iPhone individually.

I asked one of the group members to start a new group, and my name showed up in red. But when I look at the current group, the one that I started, my contact information seems to be accurate. Thank you for any help!

[Re-Titled by Moderator]