Personally, when I have this kind of thing to deal with, I don't rename all the bodies, only the ones I'm interested in, and I put the others in folders...
I know you want a standard trick to rename them en masse but if you're interested I have the following macro in stock, it allows you to mass rename all the bodies of a part to the same name followed by the increment of a counter, it's up to you to replace the base name in the NewName = "part" line.