I'm not gender neutral so I can't give advice from experience, but you do it however you feel comfortable. If you don't know what way that is yet, perhaps it's worth a shot Googling some ways others have put their preferred names into use. Tumblr, if you have it, is also a really good resource. It has a huge LGBTQ, including trans*/gender neutral, community on there. You could talk to a lot of people in the same position.
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You could also, like you said, simply change your name on your profiles and ask your friends to call you Jamie and explain to them how that name is important to you (you may have to explain gender neutral to them if you haven't already, which is a pain in the butt, but most people aren't aware of non-binary genders).
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I hope this helps a little bit, my inbox is always open (just click my username, and it's on the right) if you want to message. I hope everything works out. :)
