"Sizwe Bansi is Dead" by Athol Fugard.

This play is set in apartheid South Africa. 

At the beginning of the play, Styles (a photographer) is reading a newspaper in his studio. From his own mouth, we learn that he formerly works with Ford Motors. He later leaves the job (which he considers unprofitable) and opts for photography (his childhood hobby). 

Then Sizwe Bansi enters the studio to take a snap. He tells his own story: 

Sizwe has left his home , King William's Town, to seek employment in Port Elizabeth. A week after staying with his friend Zola, he is discovered to be an illegal immigrant and ordered to leave. Sizwe moves in with Zola's friend Buntu. 

Buntu and Sizwe are returning from a beer parlor one night when they find a corpse on the street. The dead man is Robert Zwelinzima who, unlike Sizwe, has a workseeker's permit. Buntu advises Sizwe to take up the dead man's identity but he refuses, saying, "I don't want to lose my name. What about my wife,Nowetu? Her loving husband, Sizwe Bansi, is dead! And my children! ... They're registered at school under Bansi" (page 37). 

Buntu lists the advantages: employment opportunity, regular pay, improved living standards and freedom to reside without police harassment. Sizwe eventually succumbs. He exchanges the pictures in his and Robert's passbooks. He then burns his own passbook and takes Robert's passbook and name.

So when he first enters Style's studio, he introduces himself as Robert Zwelinzima.