I believe that the law regarding names and signatures has been amended, or perhaps superseded is a better term, and it is now lawful in the United Kingdom for one to sign their name in any manner they please.

That bit of trivia aside, many peers continue to use their courtesy title after they accede to the superior title, simply to avoid social/official confusion. Virtually all peers use their title as their "last name"-- Merlin Erroll, for example, who's family name is Hay-- so His Grace is merely following social custom when he introduces himself as "Richard Buccleuth".