Tonight, I will tune my television to CBS 46 at 8:00 PM, and will leave it there until 10:00 PM. At 10:00, I'll change to the History Channel for the season premiere of Vikings. At 11:00, I'll see who Conan and Arsenio have as guests. If neither one looks interesting, I'll surf around for something that looks interesting. At 11:30, I'll check out who the guests on the main talk shows are. I'll pick the show with the most interesting guest, or if none are interesting, I'll see if there's something good on any other channel, or maybe catch up on episodes I've missed of Two Broke Girls or Mom on OnDemand.
At no point in my day will the "branding" of channel 46 have any impact at all on my viewing choices. None. Zero. Zilch. Zip. Nada. However, the programs they have on the air are very important to me. I'd watch the CBS Thursday sitcom block (unless it's repeats) no matter what they call the station.