Burne \b(u)-rne, bur-ne\ as a boy's name is a variant of Bourne (Middle English) and Burns (Middle English), and the meaning of Burne is "stream, brook". See also Calder. The baby name Burne sounds like Berne, Burnie, Burney, Burn, Borne and Byrne. Other similar baby names are Burke, Burle, Burnel and Burnet. View a list of the 3 names that reference Burne.