How to name a group text message
You can name a group iMessage as long as everyone is using an Apple device, like an iPhone, iPad, or iPod touch. You can’t name SMS/MMS group messages or iMessage conversations with just one person.
Open the group iMessage
Tap the group icons at the top of the message thread. If you have iOS 14 or earlier, tap the icons at the top of the thread, then tap the info button.
Tap Change Name and Photo
The Change Name and Photo option is in blue text under the group icons and names of the people on the thread.
Remember, you can name group iMessages, but not SMS/MMS group messages. To name a group text message, everyone needs to be using an iPhone, iPad, or iPod touch.
Add a name and photo for the group
After you enter the name for the group, tap the Camera button to take a photo. Or select a photo that you already have. You can also choose an emoji or Memoji for your group photo.
When you’re finished, tap Done.