OXM UK has discovered, Take-Two has filed trademark applications for "Rockstar TV" and GTA TV" within the past week at the United States Patent and Trademark Office, though neither has been approved just yet (nor will either be until an examining attorney is assigned "approximately three months after filing date").
Each trademark filing features identical product descriptions, denoting the filings as for (breath), "computer game programs and software; animated motion picture films featuring entertainment, namely, action, adventure, dramatic, comedic, children's and documentary themes; pre-recorded video discs and other pre-recorded digital and electronic media in the field of live action programs, motion pictures, or animation featuring entertainment, namely, action, adventure, dramatic, comedic, children's and documentary themes."
Additionally, each filing was assigned "pseudo marks" by the USPTO, referring to the "TV" part of each as "television" -- pseudo marks are not seen as definitive, but as identification marks for easing USPTO database searches. In other words, it's possible "TV" stands for something else, but we're betting against that. We've reached out to Rockstar and Take-Two for comment, but have yet to hear back as of publishing.