In 1895, the world-famous theatrical team of Gilbert and Sullivan fell apart. The partnership apparently over for good, composer Arthur Sullivan immediately began searching for a new librettist and quickly found Mr. Wilde, who had just completed an extraordinary new play, The Importance of Being Earnest, that seemed the ideal piece to set to music. If Gilbert and Sullivan hadn’t ultimately reconciled, this “what if” scenario of a Wilde-Sullivan collaboration provides audiences with a delightfully charming and frothy musical comedy.

The first scene in Earnest or What’s In a Name? opens with an account of the historic meeting between Sullivan and Wilde. At this meeting, Sullivan asks Wilde if he has any material suitable for a libretto. Wilde hands him his recently drafted The Importance of Being Earnest, and Sullivan, after reading the play’s opening, sits down at the piano and starts to write a melody for the first song (“Anyone Can Play the Piano”).

At that point, the scene dissolves into the opening scene of the “what if” musical that Sullivan might have written for Oscar Wilde’s The Importance of Being Earnest.

Act I, Scene I

Algernon Moncrieff, an idle young gentleman, receives a visit from his best friend, whom he knows as Earnest Worthing. Earnest arrives from the country intent on proposing to Algernon's cousin, Gwendolen. Algernon refuses consent until Earnest explains why the cigarette case he left in Algernon's apartment bears the inscription, "From little Cecily, with her fondest love to her dear Uncle Jack" (“My Aunt Cecily”).

"Earnest" is thus forced to disclose that he is leading a double life: in the country, he goes by the name of John (or Jack), pretending that he has a wastrel brother named Earnest living in London who frequently requires his attention; he assumes a serious attitude for the benefit of his ward, Cecily, but in the city he assumes the name and behavior of the libertine Earnest. Algernon reveals that he engages in a similar deception: he pretends to have an invalid friend named Bunbury in the country (“Bunbury”).

Lady Bracknell arrives with Gwendolen, her daughter, and invites Algernon to dine with them, but he claims Bunbury is ill requiring his immediate attention. As he distracts Lady Bracknell in another room, Jack prepares to propose to Gwendolen (“Pray, Don’t Talk of the Weather"). Gwendolyn accepts his proposal, but seems to love him only for his professed name of Earnest (“The Only Really Safe Name is Earnest”). However, Lady Bracknell discovers them and interrogates Jack as a suitor (“If Gwendolen You’d Marry”). Horrified to learn that Jack was found in a black handbag, she refuses him and forbids her daughter from seeing him. Gwendolen, however, sneaks back to the house to tell Jack that she will always love him, and asks his address in the country. When Jack gives it to her, Algernon also notes it and resolves to meet his young ward, Cecily.

Act I, Scene 2

The scene opens in Jack’s house in the country, where his ward, Cecily Cardew, lives with her governess Miss Prism. The Reverend Chausable appears and takes Miss Prism on a walk (“Will You Walk With Me?”).

Algernon arrives, pretending to be Earnest Worthing. He easily charms Cecily Cardew (“If I'm a Better Man to Be”). The young couple lose no time in becoming engaged, for Cecily also admits the name Earnest has always fascinated her. They exit.

Jack, meanwhile, has decided to put his false life as Earnest behind him. He arrives at his country house in full mourning, announcing Earnest's death in Paris to Miss Prism and Reverend Chausable (“The Death of Earnest”). At that point, Algernon and Cecily return, resulting in a clash between Jack and Algernon (“Take His Hand”).

Act II, Scene 1

Cecily, Chausable, and Miss Prism attempt to effectuate a reconciliation between the two friends (“A Sad Tale”). All except Cecily go off together. Gwendolen then arrives, having fled London and her mother to be with her love, Earnest (Jack). She and Cecily meet in the temporary absence of the two men, and each indignantly insists that she is the one engaged to "Earnest" (“Sisters”). When Jack and Algernon reappear, their identities are exposed. The men explain themselves and admit their deceptions (“Earnest Isn’t Earnest Anymore”). Lady Bracknell arrives in pursuit of her daughter and is surprised to learn that Algernon and Cecily are engaged. Her initial doubts over Cecily's suitability as a wife for her nephew are dispelled when the size of Cecily's trust fund is revealed. However, a stalemate develops when Jack refuses his consent to the marriage of his ward to Algernon until Lady Bracknell consents to his own marriage to Gwendolen (“Dear Lady Bracknell”).

The impasse is broken by the appearance of Cecily's governess, Miss Prism. Lady Bracknell recognizes Miss Prism, who twenty-eight years earlier had been a family nursemaid. One day, she left Lord Bracknell's house with a baby boy in a carriage and never returned. All is explained in the finale (“Finale”).

In the epilogue, the fate of this fictional musical that has just been enacted is revealed (“Reprise: The Only Really Safe Name is Earnest”).