Beirney \be(ir)-ney\ as a boy's name is a variant of Burney (Old English), and the meaning of Beirney is "island of the brook".
The baby name Beirney sounds like Beirne and Birney. Other similar baby names are Barney, Berny, Berne, Birkey, Birley, Birny, Bernet, Beirnie, Kearney and Verney.