A person may be known by character or by name, or by both. Jesus wants us to be recognized by character with love being the identifying trait. Since he did not give us a name as a mark of identity, we should not invent this easy route to recognition.
It is much more convenient to tell people that we are Christians, to wear a button, or to display a bumper sticker proclaiming our discipleship than to be known by our fruits. The disciples are given no proper name to wear, either individually or collectively.
My reaching the conclusion that Jesus gave us no name to wear has ruined some of my once-favored lessons concerning our new name “which the mouth of Jehovah shall name” (See Isaiah 62:1-5; 56:5). I interpreted those passages to be prophecies of the name Christian.
To support such a contention, they must be taken out of their context. In fact, in the first reference, the very text tells that the new name would be Hephzibah! The latter reference promises that their name, or heritage, would not be cut off.