Harriss \ha-rri-ss\ as a boy's name is a variant of Harrison (Old English), and the meaning of Harriss is "son of Harry".
The baby name Harriss sounds like Harris, Horace, Horaz and Horacio. Other similar baby names are Parriss, Darrius, Farris, Ferriss, Harrisson, Harrie, Morriss and Parris.