I have an iphone10 and when tap on the group icon it does not prompt to allow naming?

Hey there,

If all the members of the group message use iMessage, you can give the message thread a name. If not, then you cannot rename the conversation: Send a group text message on your iPhone Group iMessage These messages appear in blue text bubbles. They go through Apple instead of your carrier, and are protected by end-to-end encryption.

Naming a group message in Messages is only applicable for iMessage conversations. If your conversation is an SMS/MMS group message, then you will not be able to rename that group conversation. This is expected behavior and wouldn't be considered a technical issue.

Glad to hear that, your welcome ㋡