Is there a 'South Star'?
There is a "South Star" called Sigma Octanis located in the constellation Octans, but it is so dim that virtually nobody calls it the south star.
Just another side note: Polaris doesn't always point North. The reason is that our Earth has a precession effect which make the North pole circulate around the sky. This picture illustrates my point.
EDIT: Just to clarify, the picture is showing the circulation of the south celestial pole around the south ecliptic pole.
Please attribute sources of external information you include in your answers. This is where the image is taken from: https://commons.wikimedia.org/wiki/File:Precession_S.png Thanks!