Heini \he(i)-ni\ as a boy's name is a variant of Heinrich (Old German), and the meaning of Heini is "home ruler".
The baby name Heini sounds like Heinie and Heine. Other similar baby names are Heinz, Hern, Herin, Honi, Hani, Henri, Heiner, Heiko, Heike, Herne, Keoni, Meino, Reyni and Teino.