Because it's a BRAND, with some history, and viewers recognize it. And it stands for "Turner Broadcasting System" - the former owner Ted Turner. When they bought the business, they bought the name. Why should they change it? Brands have meaning to people. Examples:
1. AT&T was purchased by SBC, but they decided to use the AT&T brand. Why? Because "AT&T" was historic and more recognizable, and "SBC" didn't mean that much to people unless they were from the Southwest (originally stood for "Southwestern Bell Corporation").
2. Nation's Bank of Charlotte North Carolina bought Bank of America of San Francisco, fired all the top B of A people, and closed down the SF headquarters, and moved operations to Charlotte. So they are really not B of A, right? But they went with the name "Bank of America" because the brand was more famous, and also because it just sounds better than "Nations Bank."
3. AARP - the American Association of Retired Persons dropped the full name, and now is only known by the acronym "AARP." Why? Because many older Americans are still working, and they didn't want to seem like they represented only retired people. So why not change the name? Again - because AARP is a well-known BRAND.
Understand, now?