Anthony is the name of a servant at Merripit House. He's known the Stapletons for several years, at least since their time in Yorkshire under the name of "Vandeleur" and possibly as far back as their days in South America. (Holmes actually speculates that the guy's real name may be Antonio, and that he may originally be Spanish-speaking.) The guy has fled the country since Stapleton's disappearance, which is pretty suspicious. Holmes believes that Anthony used to take care of the Hound when Stapleton was out of town, though he may not have known what Stapleton was using the Hound for.