That's a hackamore. The bosal is the rawhide nose band, the whole lot together is called a hackamore. They are a good piece of equipment if you know how to use them, if you don’t know how to use it you will probably end up making your horse heavy headed. They are not really used to teach a horse to neck rein, however, in the advanced levels of training a horse in a hackamore you may well teach them to neck rein with it. The main point of them is that they are a part of a training system for teaching a horse to work which has the long term aim of getting them to eventually work in a full bridle; the idea being that you teach them everything they will ever need to know in a hackamore (or really a series of them) then, when they are a good going horse, weaning them off the hackamore into a bridle. Having said that though, if your horse goes well in a hackamore you can just ride them in it indefinitely, generally speaking.
Yeah I would not teach to neck rein in the hackamore.
I love to show in one on a junior horse, however I know a lot of people do not know how to use one properly and have indeed made their horses hard in the face. My gelding is an example, he came to me "hackamore broke" whatever they meant by that, and was bracey, hard in the face, pushy, no respect for it at all, couldn't get him stopped or listening at all. Three years later, he can be ridden in one again. It is far easier to play it safe than to put a horse in equipment like that unsurely and ruin him, because then someone will have to rebuild it.
So, if you choose to go that route, have a trainer help you out. That's my advice anyhow.