Thanks for reaching out to the Apple Support Communities.
I understand that you're unable to name a group message. I'll be happy to help.
If this group message contains a user or users who do not have an iPhone and aren't using iMessage, then you won't be able to name the group. You can name only group iMessages.
Please see this support article: Send a group message on your iPhone, iPad, or iPod touch , specifically:
Name your group conversation
Have multiple group iMessages? Name your group iMessages so they're easier to find. To name your group:
You can name only group iMessages, not MMS group messages.
Let me know if you have any questions.