A synced group chat is automatically created whenever a Group is set up, and its membership stays in sync with that Group. Its chat name and photo can still be customized on their own, separately from the Group's name in Groups management.
Open the synced group chat.
Tap the group chat profile.
Tap Edit next to the chat name or photo.
Update the name and/or upload a new photo.
Tap Save.
Note: Changing the chat's name or photo here only affects how the chat displays. It doesn't rename the Group itself, membership and admins for a synced chat are still managed from the Group.