Some very good ideas are coming out of this thread. I'd like to make a few observations about what's being proposed.
In my mind, the Pirate Party has always been about freedom and equality. Freedom without equality isn't fantastic, and equality without freedom is possibly worse. The result of freedom and equality is participation. Participation in society, culture, the economy, politics and in civic life. And participation means democracy, ultimately.
So what I think we need to capture in a name is at least freedom and equality, and possibly participation if we can stretch that far. I think we should also avoid meaningless words that don't add to the 'honesty' of the name. We also need to avoid words that are narrower than 'Pirate'.
'Libertarian Left' captures freedom and equality, so finding acceptable alternatives for those two words is what we're after, I think.
Words for freedom: civil liberties, human rights, libertarian
Words for equality: fair go, equity, commons, common, 99/99ers, collective, social, left, egalitarian
Words to avoid because they are either meaningless, narrow or inaccurate, or all three: progress, progressive, future, Internet, open source, open, democracy, raising standards, people, next, tomorrow, growth, digital, privacy, transparency, government, freedom of speech, anti-censorship, evidence-based, 21st century, copyright, reform, new deal, Australia, centre, merits, independent, basic income, agitator, federalist, roots.