When this short story begins, it focuses on Gurov, who has just become aware of this mysterious woman and her pet dog. As Chekhov writes, "No one knew who she was, and every one called her simply 'the lady with the dog'" (1.2). Later, after Gurov and Anna sleep together, he looks at her and recalls the label of "the lady with the dog" (2.1). At this point, we see a rift between the snapshot of Anna from that first paragraph and the woman Gurov now realizes her to be.
And indeed, these shifting perceptions are a main theme in "The Lady With the Dog." A large part of Gurov's transformation (see his "Character Analysis" for more) has to do with his changing the way he sees Anna, from yet another sexual conquest to the only real love of his life. So when we return to the title, for the third time, in the third section of the short story ("So much for the lady with the dog… so much for the adventure…"), we can assess the differences between the Gurov of that first paragraph and the Gurov who now looks back at that initial encounter (3.22).