Well, “natural-sounding”. That sounds extremely subjective to me. I guess everyone has his/her own opinion about what “sounds” natural, sometimes even amongst native speakers. Do you have any better criteria to nail it down? That would be helpful.

I try to explain the sentence: This sentence means that the speaker has a name, but he/she does not say that name, but only says that the name has a name. And the speaker says that the name of that name is “Strange”.

This is not even a literal translation.
But if you have a better way to express this, please share it!
If you think the sentence is so bad, just delete it.

I also have written a lengthy comment (in English) about nonsense here: http://tatoeba.org/deu/sentences/show/3761259
(I also quote Through the Looking-Glass (a nonsense novel) by Lewis Carrol, maybe stuff becomes clearer here.)

If someone studying English memorized this sentence pattern thinking it was something we actually used, then tried using it with a native English speaker, that native speaker would assume that the non-native speaker still wasn't very good at English.

Perhaps another member can explain the aims of the project to you better than I can.
I'm not sure how else I can explain it.