From First and Second Peter, Jude (Coming November 2011) by Daniel Keating, commenting on 1 Peter 4:16:
But whoever is made to suffer as a Christian should not be ashamed but glorify God because of the name. Here Peter restates what he just said about being “insulted for the name of Christ,” but now he uses the term “Christian” to identify those who are suffering. Apart from two appearances in Acts (11:26; 26:28) this is the only occurrence of the term “Christian” in the New Testament. It is likely that “Christian” was originally a term of derision and abuse employed by those who opposed Christ’s followers. But now, Peter says, it is to be received “without shame.” When we are abused and reviled as Christians, that is, as followers of Christ, then in fact we are bringing glory to God (see 4:11).