According to Wikipedia, the Brandenburg family is part of the house of Hohenzollern. But the first Zollern is in the 12th century (http://en.wikipedia.org/wiki/Frederick_II_of_Zollern). All his ancestors are named Brandenburg, and before that Nürnberg.
Is it OK to use Brandenburg as LNAB ?
(Hohen) Zollern. The family began with Friedrich I about 1085. althouigh the first mention is reckoned to be 1061.
http://daten.digitale-sammlungen.de/0001/bsb00016326/images/index.html?fip=193.174.98.30&id=00016326&seite=512
The question is how thre change to Brandenburg, came about. The Great Elector was Elector of Brandenburg, which is a title not a family. But the name seems to have taken over. I think I'd go woth what they saw themselves as.