I'm open to the idea that some things are unnameable but would need an example :)

I'll write you as soon as I can

The Herzbergers' paper: https://sci-hub.ru/10.1007/BF00202726

If we assume the real numbers exist, then perhaps the paradox resolves because there are uncountably many reals and only countably many nameable things, but then perhaps the paradox does not resolve because we assume ZFC is true and we can well order the reals, hence name the first unnameable real.