No, it's the leader. We don't call it a hook-length although in fly fishing terminology this is basically what it is.
Often we use a knotless tapered leader with a short length of "tippet" at the end which carries the fly.
If you are really keen to get started at fly fishing I would suggest you get a book on the basics. There is a lot of new terminology you are going to have to learn. My suggestion is to phone "Trout Fisherman" , a magazine produced by Emap, the same company that produce Angling Times. I am sure they will recommend a suitable book, but they will also suggest that you have a few lessons with an APGAI instructor.
Seriously, this is money very well spent.
Sessions cost about ?35 an hour.
The main difference between fly fishing and general coarse fishing is that you will enjoy fly fishing a hell of a lot more when you can cast well. It's a bit like golf in a way. This is the main hurdle the newcomer to fly fishing has to overcome.
Casting a fly is totally different to casting a float, feeder, lure or leger. You are not actually casting the fly at all, you are casting the line, the fly goes along for the ride.