He discovers his name is Ernest. Jack hugs Gwendolen joyfully, knowing they can finally be married. Jack tells Lady Bracknell he has learned "the vital Importance of Being Earnest."

Are Jack and Gwendolen cousins?

Jack turns out not to be the son of some random rich merchant (which would anger his potential mother-in-law, Lady Bracknell), but a legitimate aristocrat. In fact, he's Lady Bracknell's nephew and Algernon's older brother. This makes him Gwendolen's cousin as well as lover. ... So Jack/Ernest and Gwendolen get together.

Is Jack in love with Gwendolyn?

Gwendolen is in love with Jack, whom she knows as Ernest, and she is fixated on this name. This preoccupation serves as a metaphor for the preoccupation of the Victorian middle- and upper-middle classes with the appearance of virtue and honor.