I'm A Stranger Here Myself and Other Stories — Craig Rice

Charlie Bekker -- also known as Bob Smith, J. Brown and Will Jones -- one morning finds himself in a very sticky situation: he wakes up on the floor of an unfamiliar room, under circumstances he couldn't recall, with a girl he has known only in passing. And the girl is dead.
But by some good fortune he happens to bump into John J. Malone, Chicago's best criminal defense lawyer, who agrees to help him get out of the mess. But the multiple identities starts getting on his nerves, as well as the web of deceit and deception, and the growing number of people getting uncannily involved in the whole thing.
Will the great John J. Malone be able to survive this … or will this be his last case?
Also includes the stories: THE TEARS OF EVIL, NO VACANCIES