Staunton \s-taun-ton, sta(u)-nton\ as a boy's name is a variant of Stanton (Old English), and the meaning of Staunton is "stone settlement".
The baby name Staunton sounds like Stanten and Stanwood. Other similar baby names are Swanton, Danton, D'anton, Dunton, Stockton, Swinton and Tanton.