To send a group message you need to send a message to a set of friends and then you can name the conversation. At no point a group is created on your contacts
Use third party apps for creating groups.
Send a group message
- Open Messages and tap  to start a new message.
- Enter the recipients' names or tap  to add contacts.
- Enter your message, then tap Send .
To send a group MMS message on an iPhone, make sure MMS Messaging is turned on. Go to Settings > Messages and turn on MMS Messaging.
Name your group conversation
Have multiple group iMessages? Name your group iMessages so they're easier to find. To name your group:
- Tap a group conversation, then tap the top of the conversation.
- Tap .
- Tap Enter a Group Name.
- Enter a name, then tap Done.
You can name only group iMessages, not MMS group messages.