I think the only words that take no articles (a/an/the) ever are proper nouns ("A Cindy"; "The Canada").
Mass nouns or noncountable nouns such as furniture and data can't be expressed as "A [noun]" but as "A [unit] of [noun]", as in "A piece of furnitune", but "the furniture" works.
Come to think of it, I am coming up with some proper nouns that can take a definite article (the) but they're mostly brand names used in place of generic terms.
I'm not sure if there's any sort of noun that never takes an article or what it would be called.
I don't think there is a term for that. Any noun sounds "right" when you put "a, an, the" in front of it. However, in sentences, by custom, we put an article before some nouns in some uses, but not in others. This is very difficult for ESL students. For instance, we say, the Second World War, the Civil War, but World War II.
I taught my students that if "the, a, an" didn't sound right before a noun, that probably it was not a noun but another part of speech. We don't say "the is," "a think," or "the after."