The claim is false. There is not a thing that cannot be given a name. If it is a thing, it can be given a name. You take that thing into the discourse and say, "let this thing be X", and now it has a name. What cannot be given a name cannot be discussed in any way; it is completely vague, undefined or ephemeral. The inability to name it is not what is at the core of not being able to pin it down; it is a byproduct or…
You didn't name the object when you said "let this thing be X"; you actually had already identified that "thing", and that process of identification was the process of naming it. You then defined some syntax ("X") and said that it was a name. But there are things for which you can't even say "let 'this thing' be…". For example, ZF proves that there are uncountably many reals. There are only countably many names, so t…
No, it wasn't. Entities can be identified without being named, by relationships to other entities and class and such. That identification requires words. Not all denotational words and phrases constitute names.