This is a very good question. Some writers give a great deal of attention to naming their characters, while others do not. Saki seems to be one of those writers who uses characters' names to convey impressions about them. Framton Nuttel is certainly an unusual name. The first name, Framton, suggests that this man is one-of-a-kind, strange, an unusual person, both in his manners and his appearance. It may suggest that he is fragile--or something like that. The last name, Nuttel, certainly suggests that the man is a little bit nutty. He is obviously neurotic. The two names together sound comical, and we readers probably see him as comical from the very beginning. When he makes his desperate retreat from the house, we see this as comical because he is a comical character.
Mrs. Sappleton's name suggests that she is not too bright. The name hints that she is a sap. She needs to have that characteristic in order to play the part that her niece Vera has created for her. Vera's name suggests that the girl is truthful. She is certainly not that! But the name may help to beguile Framton, and it may also help to beguile the reader for quite a large part of the story.