Not even damaged...![]()
Edit:
Now if you look at this image you can see that Zaraki's soulslayer doesn't look like a normal, sealed one: It has a white bandage wrapped around its handle like Ichigo's constant released shikai-zangetsu and its guard doesn't look normal, too. Not to speak of its damaged style that fits Zaraki's scar-addiction pretty well.
Now I'm not sure about this but didn't Kenpachi say his sword doesn't even have a name? Maybe he simply is going to give it a name himself - just as he did with his own and Yachiru's name.