https://3quarksdaily.com/3quarksdaily/2014/03/boundaries-and... This is a beautiful article on the subject.

To prove that there are unnamable concepts, he uses cantor's diagonal argument. There are countably infinite names. Any subset of these names is a concept, which is same as the powerset of the set of names, and through cantor's diagonal argument, there are uncountably infinite concepts, most which are not namable.

Yes you can take a specific concept, and name it, but there are uncountably infinitely many, so even with infinite time, you cannot name them all.