I suppose I had been a little harsh the other night. So, I wanted to take a moment to apologize.
I know you have been trying to investigate set theory in relation to mereology.
But, if you are going to pursue this use of a 'name' relation, you should take the time to look at some of the web pages to which I directed you. Whether or not David Lewis is using a formal symbol conveying the sense of a name, there is a relevant body of philosophical inquiry that applies.