Burnis \b(u)-rnis, bur-nis\ as a boy's name is a variant of Burns (Middle English), and the meaning of Burnis is "brook". The baby name Burnis sounds like Bernis, Barnes and Byrnes. Other similar baby names are Burnie, Barnie, Barni, Baris, Bernie, Burney, Birnie, Boris, Borris, Burne, Burn, Burgiss, Burges, Burnel and Burnet.