There's no character or significant element explicitly referred to as "Else" in Katherine Mansfield's short story "The House." The story focuses on the alienation and emotional disconnect within a family dealing with the death of a child and the subsequent sale of their home. There are no characters with that name.
It's possible you're misremembering the story, confusing it with another work, or perhaps recalling a different detail. Could you be thinking of a different character's name, or a different story altogether?