How can I send a group message whereby the recipients only see my name?

As of iOS 17, it's no longer possible to send a group message on iPhone whereby the recipients only see your name.  As a workaround, A2Z Contacts allows you to send a group message whereby a separate message is sent to each recipient. To do so, open A2Z Contacts, go to Group Text, and when you reach the "Compose Message" screen, set the "Max Recipients Per Message" to 1.

iOS 18 introduces RCS messaging, a superior alternative to SMS. RCS is a much richer standard. It may eventually be possible to send group messages using RCS such that the recipients only see the sender's name.