I'll assume you hit the first fork in the river above the parking area. If so, to answer your question after the forks end, you're still on the Greenbriar. Just after the forks end, you'll enter the Greenbriar Gorge which goes all the way to the point where the Ramsey Prong empties into the Greenbriar. The Gorge is one of the most beautiful areas in the Park IMO, I usually fish it once or twice a year. Note: once you commit to the Gorge you have 6-7 hrs of fishing ahead of you until you reach the mouth Of Ramsey Prong. It is a rough area to fish, large boulders and swift water abound. It is best to fish this area when water levels are normal or maybe a bit below normal. It's a great place to fish in summer, I fished it nearly two weeks ago, and water levels were perfect for fishing. If you've never fished this are before, it's best to take a buddy and let someone know where you're going to be fishing. Brookies become more prominent as you head upstream.
Once you reach where Ramsey Prong enters the main stream on the left, the main stem continues on the right. This is some of the better water in the Park for brookies, but it is not for the faint of heart as there is no trail along this stretch of the river.