What is this cogset body? I have some backlash (free movement) in my body of cogset, so I try to dissemble my cogset to discover this weird body:




I'm trying to find a new one but I don't know how to call it. Any idea how it can be called ?

(Sorry, I'm french, I try to find translation for word, but I hope the picture help)
That's a freehub body. 

Look on the hub for the model of hub you have, and then you can use that to find the appropriate freehub body model by looking at the documentation of the hub.