Why does Jack establish two different identities for himself—one for the country and another for the city? So that he can take a brake from being a guardian in the country. When he is bored, he goes to the city to help his “brother” Earnest, but he is really just having alone time.

Why does Jack Ernest have a double identity when does he finally disclose it?

Jack Worthing calls himself “Ernest” instead when he is in London because his “brother” that he came up with is full of mischief and misbehavior, so Jack is able to escape to London and misbehave on account of his brother.

What is the significance of Jack's leading a double life?

The double life led by Algernon, Jack, and Cecily (through her diary) is simply another means by which they liberate themselves from the repressive norms of society. They have the freedom to create themselves and use their double identities to give themselves the opportunity to show opposite sides of their characters.