I live in the US and knew a kid named Fox. Even though my dad watches Fox News, the association never crossed my mind. (I'm more of a Daily Show/ Colbert Report fan myself.) There could be parts of the country that are as strong against Fox as we all are about Benedict, but I don't see it as being a huge problem like you. I see it as an adjective name (short for Foxy) or an animal name (Leo, Bear, Hawk, Snake).
ETA- My dad used to work at a company called Fox, assembling farm equipment. I live near the Fox River, and a group of cities and towns on it is collectively called The Fox Cities. The minor league baseball team there was the Appleton Foxes. A mall there is Fox River Mall. Like another person added, Fox Mulder from The X Files. There are enough associations for foxes that the news channel isn't strong.
This message was edited 1/4/2015, 9:20 AM