The thing is that the Pirate movement was named so by it's opposition in an attempt to discredit us long before there was a Pirate Partly.
So when Rick Falkvinge was about to start a new party in early 2006, he knew that our political enemies would call us pirates no matter what we called ourselves, and decided that it was better to reclaim the name than to be ashamed of it, much like what the HBT-movement have done with "gay".
(As a side note, the first organization using the word Pirate in their name in reference to online piracy was the Swedish MPAA equivalent "Antipiratbyrån" (The Anti-Pirate Bureau), which was formed in 2001. The Swedish pirate movement didn't get organized until 2003 when the think tank "Piratbyrån" (The Pirate Bureau) was formed as a direct response to the lobbying by Antipiratbyrån. The bureau picked its name for contrast, and succeeded in building enough brand recognition in Sweden to make the original Pirate Party a well-known name within months of being founded, despite our next-to-nothing funding. No other name would have given a better start, and trying to re-brand now, after gaining just enough mindshare to be elected, would be suicidal)