Just did a Google search...
I have just posted an e-mail to James Kaler, who seems to be the source of the name - presumably written in his book "The Hundred Greatest Stars".
He claims this was assigned in 1700, but there is no reference backing this up. The only southern observer positioning these stars was Lacaille, who did so in the years 1751-52.
Kaler also mentions this name as a casual quip in his "star" webpage
http://www.astro.uiuc.edu/~kaler/sow/polaust.html
The definitive source of Star names is Richard Allen's "Star-Names and their Meaning" (1899). he does not mention sigma Octanis at al in pages 296 and 297 on the constellation. As the constellation was named by John Hadley in 1730 - makes the Polaris Australis name even more doubtful being named 30 years earlier. Even so, this would suggest that any such name would have been added in the 20th Century!
As for the Brazilian flag. The graphic of the sky represents the sky as seen from Rio de Janerio on 15th November 1889 at 08:30 a.m. when the Constitution was signed. Sigma Octantis ("σ" Octantis; south pole star) was supposed to represent the central capital of Brazil. The document of the introduction of the flag, written in Portuguese, only references the star as Sigma Octanis - and nothing else. This is also discussed in "Os Símbolos Nacionais"
(The National Symbols) of 1986 - stating the same.
As for the need for a southern pole star, would have been unnecessary, as the sailors would use the Southern Cross longest axis. The Cross would have been used, only because sigma octanis would have been invisible to the unaided eye in poor conditions.
These are my reasons I think the usage is very doubtful...
Andrew
NOTE: You can read a more extensive appraisal of finding south, using the Cross (and other means) at my trial pages for my website at;
Guide to the Southern Cross at;
http://au.geocities.com/ariane2au/PageSCross001.htm
Finding South
http://au.geocities.com/ariane2au/PageSCross004.htm
and
http://au.geocities.com/ariane2au/PageSCross005.htm
With the changes of the Cross due to proper motion through the millennia at;
http://au.geocities.com/ariane2au/PageSCross006.htm