As long as the station uses the callsign/city of license once per hour on all subchannels in visual or audio form, they are in compliance. For example, WXIA/Atlanta does not use the COL on their former WeatherPlus channel, and is using WXIA-DT rather than their assigned WXIA-TV, so they have been in violation for a while now (callsign rules changed with the June 12th analog shutdown).
Outside of that...the FCC has no jursidication on how a channel brands, as long as the branding itself is not indecent or obscene.