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.