I don't pretend to fully understand what transgender teenagers have to go through. But, I still can't help but feel like I'd have to be very hesitant about going through with any permanent procedures. I was a teenager too once, and I shudder to think of what would have happened had I been able to carry out everything I felt was an existential need when I was 15.
But of course I would take it seriously. I would absolutely support decisions to take on a different-gendered name and approach a different role (ie clothing, etc), and I would be okay with beginning a conservative (as in, medically conservative, meaning careful and non-committal) approach to reassignment to reduce the problem of lost time (the earlier the reassignment process begins, the better, being my understanding). I would say that I'd expect to hear from at least one therapist, ideally more than one, that the kid really wants it, that it's a rationally-made decision, and s/he would benefit from a permanent reassignment.
Now, I've read the literature on people who regret gender reassignment. It's a very low proportion, reported generally to be somewhere around 2-5% (very low for elective procedures) because, duh, it's not something you do on a whim like trying on a new coat, you don't wake up in the morning one day and say "You know what, today I'd like to change gender." But that's still a non-zero number, and it's a permanent procedure, so I want that risk to be as low as possible.