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.