Well, first of all, we don't need an article before any noun. I can say:
I like dogs.
As to your question of why, the answer is, "because that is how English works".
The articles perform a discourse function, by indicating new and old information. They often evolve from demonstratives (e.g. "this" and "that"). They evolve independently in unrelated languages. Normally, once an article system becomes a part of a language, it is an all-or-nothing thing. This is not unlike a verbal inflection system, a gender system, or a case system; once the system is in place, it is not optional.
Aside from this, there isn't really a more concrete reason for "why" English works this way.
House style prevails. How does the organization refer to itself? Do they provide identity guidelines for third party media? Nearly all newspapers take the, but there are as many exceptions as there are rules when it comes to applying articles to named entities.
Certainly, if it is part of the official name, it would always be included except where attributive: The New York Times, The Telegraph; but New York Times columnist Thomas Friedman and Telegraph motorcycle correspondent Kevin Ash.
In other cases, the article is not part of the official name, but it gets attached idiomatically: She writes for the Chicago Tribune, I subscribe to the South China Morning Post. Perhaps this is because many publication names are based around a common noun, and we naturally add the to most such names: The Wall Street Journal, not merely any Wall Street journal, same as the Royal Society, the University of Virginia, the Brisbane Lions, or the Socialist Republic of Vietnam.
Newspaper names not based on this formula (the Foo Newspapertype) do not accept articles: Barron's, never the Barron's, as with Roll Call, USA Today, Stars and Stripes, and so on.
But then there's Sporting News, never the Sporting News, because that is their house style. And JAMA is always simply JAMA, even though the full, official name is JAMA: The Journal of the American Medical Association.
See also
Best Answer
Like any rule in English, there are many exceptions.
Generally we use "the" when the mountain is one of the earlier named Alpine German loanwords -- the Matterhorn, the Jungfrau, and so on. In these cases, the mountain's name tends to be self-descriptive (e.g. Matterhorn means "meadowed peak" in German, so "the Matterhorn" is talking about a specific one and not a general "meadowed peak"). But that's just an observation, not a rule.
We can also use "the" when talking about a collection of mountains (either a full mountain range or just a group of mountains) -- the Cascadia Range, the Blue Ridge Mountains, or the Himalayas.
Sometimes we omit the article altogether: he managed to climb Everest last spring.
Here's one rule that is pretty reliable: we don't use Mount and also an article. So you probably wouldn't see, e.g., "the Mount Matterhorn" or "the Mount Everest".