A name change will do more harm than good.
While it certainly could be harmful, I'm not convinced that it necessarily would be.
I've seen something similar in recent years which backs this up: In the ancient days of the late 70s, RuneQuest was released (a tabletop RPG, for anyone unfamiliar with the name). Its fortunes rose and fell, but it stuck around well enough that, some years ago, RuneQuest 6 was released. A couple years later, ownership of the "RuneQuest" trademark changed hands and the new owners chose to withdraw RQ6's license to use the name so that they could create their own new edition of RuneQuest which returned to the game's roots, as RQ6 had grown to be a very different beast from the earlier editions of RQ. Not wanting to abandon their work, the authors/publishers of RQ6 renamed it "Mythras".
The renaming of RQ6 to Mythras has caused no harm to the game or its publisher, despite the fears of many of its fans (myself included). There were a couple years of people referring to the game as "Mythras (formerly RQ6)" for audiences who might not be aware of the name change, but Mythras is getting to be known well enough under the new name that this practice seems to be dying out. Really, the only ill effect I can see to the change is that it's less googlable, since, unless you're careful with your search terms, you'll get more hits for Mithraism than for the game.
Now, granted, RPGs and programming languages are different and the Perl 6 name has been around a lot longer than the RQ6 name was, but P6 has also gotten a lot more bad press than RQ6 did. I don't claim to know where the balance would be likely to end up between the harm from lost name recognition and the gain from distancing the language from that bad press.
In the end, though, as you reminded us, Larry doesn't want to change the name and he has the last word on it, making all of this academic.