Appel's note 253/1 (pages 429-30 in The Annotated) seems relevant here. He writes, "Nabokov immediately mocks such doggedly persistent literalism by having H.H. hire Bill Brown, an imbecilic private detective...a gesture that can only be for the benefit of the literal-minded reader."
 
Unless I'm missing something, Bill Brown is not the name of the private detective, but rather the name of the person that the detective tracks down: "he turned up one day with the triumphant information that an eighty-year-old Indian by the name of Bill Brown lived near Dolores, Colo." (253) Even so, I wholeheartedly share Appel's conclusion that "Nabokov ... mocks such doggedly persistent literalism": "The 'information' provides a non-solution that parodies the reader's need for a solution and our belief that either literature or life will ever reveal one." I also appreciate the mention of the corrected hyphen.
 
Bruce