Actually the abbreviated form of "Port Authority Transit," the port authority in this case being the Port Authority of Allegheny County."
In late 1998, they decided to reimage themselves, changing their name from PATransit to "Port Authority Gold," the idea being that they were providing the gold standard in public transportation service. It also doesn't hurt that, for many Pittsburghers, the color gold brings to mind the beloved Steelers, Pirates, and Penguins, since all three teams use a black and gold color scheme.
However, "Port Authority Gold" doesn't sound like the name of a transit authority, it sounds like the slogan of a radio station. At one point, I tried to come up with a supposed playlist for Port Authority Gold, but I couldn't get beyond the Hollies' "Bus Stop." This is because there aren't any songs about the 42S light rail line to South Hills Village, as far as I'm aware.