Hi Jean Z,
I understand that you're trying to change the name of a group message, but you're not seeing the option to do so. I'm happy to provide some help for this issue.
In order for this to work, the conversation needs to be a group iMessage. While your friends are all using an iPhone, they need to have iMessage enabled and the conversation needs to be using their contact method for iMessage. You can use the information in the article below to discover if you are indeed in a group iMessage:
Send a group message on your iPhone, iPad, or iPod touch - Apple Support
The three types of group messages that you might see are: group iMessage, group MMS, and group SMS. The Messages app automatically chooses the type of group message to send based on you and your recipients' settings, network connection, and carrier plan. For example:
- If you and your recipients are using Apple devices and iMessage is turned on, then the group message is sent as an iMessage.
- If you send a group message to people who aren't using iMessage, then the message is sent as an MMS or SMS message.
These messages appear in blue text bubbles, go through Apple instead of your carrier, and are protected by end-to-end encryption. In a group iMessage, everyone can:
- Send and receive photos, videos, and audio messages
- See all responses from the group
- Send and receive message effects, like sketches, animations, bubble effects, and more
- Share their location with the group
- Give the group a name, add or remove people from the group, mute notifications, or leave the group
These messages appear in green text bubbles and go through your carrier instead of Apple. In a group MMS, everyone can:
- Send and receive photos and videos
- See all responses from the group
- Mute notifications
These messages also appear in green text bubbles and go through your carrier. Group SMS messages don’t support multimedia attachments, like photos or videos. All responses in a Group SMS are sent as individual text messages and the recipients can’t see the other responses from the group.
Learn how to send and receive iMessage, MMS, and SMS messages on all of your Apple devices.
Thanks for using the Apple Support Communities. Cheers!