In Julius Caesar, the poet killed by the mob is Cinna.
Cinna appears after Caesar's funeral, when an angry Roman crowd is hunting people associated with the assassination. The citizens question him about his name, destination, and political allegiance. Although he clearly explains that he is Cinna the poet rather than Cinna the conspirator, the mob attacks him anyway.
The scene depends on a deliberate identity mix-up. Cinna the conspirator is one of the men involved in Caesar's assassination, while Cinna the poet has no part in the conspiracy. The crowd first calls for him to be torn apart as a political enemy, then says that he should be killed for his bad verses even after hearing that he is a poet.
This brief episode shows how quickly public anger becomes irrational violence after Antony's funeral speech. Messala, Lucilius, and Titinius belong to the later military and political action, but none is the poet killed by the mob. Shakespeare drew much of the play's historical material from Plutarch.