I'm also transgendered and have being dealing with it since I was very young. I am biologically female though, so I imagine it has been somewhat easier on me than for your son, although there is still a lot of discrimination. I think its wonderful that you are trying to do the right thing and allowing him to explore who he is. My own parents tried to force me to dress and act feminine and it only caused a lot of tension and fighting. I still don't feel like they fully understand.
I do have a few concerns about your son. I know when I was 16, I wanted things that I do not want now. At the time I thought I wanted gender reassignment surgery for instance. As I've grown older, I've realized that its a really big decision, and I'm probably not going to do it. I would say that my attitude in regards to my gender has changed quite a bit since I was 16. I think allowing him to legally change his name is a really big step- although it is, of course, reversible if he would so choose in the future. He may not want that in a few years time.
Also, you say you tried counseling and it didn't work. What happened? What went wrong? There are counselors who work with transgendered youth. There are also counselors who seek to impose the "proper" gender role on such children. I can see how the later might not have worked out so well. But there are counselors who can sit down with your son and explore this with him and to guide him through the process if he so chooses. Even if the counselor was perfect, sometimes the personalities just dont match well- would he be willing to try with a different person? Maybe allow him to be part of the process in finding a new one so he feels comfortable with who he sees? (I always hated the counselors my parents picked out on their own) Don't frame it as a punishment or as there being something "wrong" with him- being transgendered is hard, kids tease, society doesn't understand, people try to make you conform to a gender that feels wrong, and it can be very confusing to understand exactly who you are through all of it. I would frame it as someone he can talk to to help him deal with working through this and dealing with how others react. You can find lists of therapists who work with transgender youth on the internet. If there is a gay community near you, or a PFLAG, or a college campus with a gender studies department or a gay student group, they can also point you towards local resources. Some larger cities even have transgender support groups, if there is a large city near-ish to you, you might see if they do, and the organizers may be able to recommend local resources.
If it were my son, I would probably find him some supportive counseling with a therapist experienced in helping transgendered youth. They'll know how to help him deal with his peers, and also how to help him think through big decisions like this. Generally, treatment standards call for a period of time living with the decision before making it permanent- in this case, he would be called Emma for a period of time before legally changing his name to be sure he fully experienced and understood the consequences of the decision. I would suggest you call him Emma for a time first. You have a few years before you have to worry about graduation. Getting the school to agree to it may be tricky though, which is why having a good therapist is important- they can be a professional advocate for your son in that area.