It depends on your state. But considering you just came out, and I'm assuming you haven't been to a medical professional, I'd safely say no for the gender marker. Name change can occur anytime, you just need to talk to your parents. It may take a few months for it to go through, but it is relatively straight forward.
For now, find a good gender therapist. Try contacting your local LGBTQ support center, if you have one, and they might know. Skype is also an option, and my therapist is amazing. He isn't a gatekeeper, he is only there to help you successfully transition.
http://therapists.psychologytoday.com/rms/name/David_Baker-Hargrove_PhD,LMHC,DAPA,CCFC_Orlando_Florida_45705So, you have the support of family, now do something. Get your letter for HRT, then find an Dr who will prescribe HRT. That might somewhat trick at your age because some people see it as controversial, but you should be able to get on testosterone blockers at the very least. And trust me, that will be more precious than gold to you at this time. Above all else, be proud of who you are, and that you are leading life by your terms.