I'm informed that it's actually a contraction of " pen" and "garth" , where a garth is a promontory, a sticking-out bit of land. (I previously thought its derivation was as you said. And we won't let this get in the way of a good pub name!)
Other examples of the word include the Garth area of Bangor, where the pier extends from, and of course Gogarth (the Great Orme). The prefix "go-" is a superlative here, i.e. the Gogarth is a great big promontory!
For context, others are worried at Welsh placenames disappearing or being excised by new placenames. Not settlements, by and large, but certainly landscape features (hills, valleys, bays) and names of old farms and houses. I wouldn't be surprised if the councillor that made the above request to the National Park did so with this very issue in mind.