In plotting his story, Saki must have given lengthy consideration to the questions of who would greet Framton and what that character would tell him. Framton probably expects to be greeted by Mrs. Sappleton, but there was no way that Saki could get this lady to tell a wild ghost story. It seems plausible that Mrs. Sappleton would send her adolescent niece down to get a little experience playing hostess, and it also seems plausible that Vera would resent being employed in that role. Vera is young and mischievous. She doesn't want to be turned into another hothouse flower like Mrs. Sappleton. Vera knows she is being prepared for a dreary future in which she will become a country housewife who has little to do but make small talk and serve tea. Saki characterizes Mrs. Sappleton brilliantly in one sentence:

"No?" said Mrs. Sappleton, in a voice which only replaced a yawn at the last moment.

No doubt the aunt has had to suppress many yawns over the years.

Vera knows that Framton doesn't have to be greeted the moment he arrives. He could be left to sit there for the few minutes it takes her aunt to arrange her hair and powder her nose. As as fictional character, Vera is a good creation. She makes an excellent contrast to Framton, so that it is easy for the reader to picture the two of them and even to imagine the sounds of their voices. Framton is a nervous wreck, Vera is consistently described as cool and self-possessed. Sakl actually uses the term "self-possessed" three times in describing her; this is to prepare the reader, as well as Framton, for the change when the precocious girl pretends to be amazed and terrified by the arrival of the three hunters outside.

The child was staring out through the open window with dazed horror in her eyes.

Vera is young, Framton is middle-aged. She is a female, he is a male. He is nervous, she is relaxed. We can imagine her half-reclining on the sofa, while we can imagine the visitor, dressed in tight-fitting formal London attire, perched on the edge of his chair.

The reader doesn't actually realize that Framton has been taken in by Vera's ghost story until almost the very end of the story when Mr. Sappleton enters.

"Here we are, my dear," said the bearer of the white mackintosh, coming in through the window; "fairly muddy, but most of it's dry. Who was that who bolted out as we came up?"

Frampton Nuttel is the protagonist of Saki's short story "The Open Window." In this story, Frampton is traveling in order to find a quiet repose (one which will help calm his nerves). The opening line of the story defines the person Frampton first meets as he arrives at Mrs. Sappleton's home. 

The niece of Mrs. Sappleton is the first person Frampton meets. Readers are left uninformed about the name of the niece until Mrs. Sappleton enters the room, well into the story. Vera is the niece of Mrs. Sappleton who first meets Frampton, invites him into the house, and weaves a tale of utter horror. 

In the end, readers come to find out that Vera is not a very friendly young girl. Instead, she proves to be quite the trickster.