A.T. Robertson Commentary 1 Peter 4:16

"but if [a man suffer] as a Christian, let him not be ashamed; but let him glorify God in this name." — 1 Peter 4:16 (ASV)

But if as a Christian (ε δε ως Χριστιανος). Supply the verb πασχε (condition of first class, "if one suffer as a Christian"). This word occurs only three times in the N.T. (Acts 11:26; Acts 26:28; 1 Peter 4:16). It is word of Latin formation coined to distinguish followers of Christ from Jews and Gentiles (Acts 11:26). Each instance bears that idea. It is not the usual term at first like μαθητα (disciples), saints (αγιο), believers (πιστευοντες), etc. The Jews used Ναζωραιο (Nazarenes) as a nickname for Christians (Acts 24:5). By A.D. 64 the name Christian was in common use in Rome (Tacitus, Ann. XV. 44). Owing to itacism it was sometimes spelled Χρηστιανο (ι, ε and η pronounced alike).

Let him not be ashamed (μη αισχυνεσθω). Prohibition with μη and present passive imperative of αισχυνω. Peter had once been ashamed to suffer reproach or even a sneer for being a disciple of Christ . See the words of Jesus in Mr 8:38 and Paul's in 2 Timothy 1:12. Peter is not ashamed now. In this name (εν τω ονοματ τουτω). Of Christian as in Mr 9:41, "because ye are Christ's."