I did a new profile for facebook, but for Linkedin I just changed my name. That went well. No one said anything good or bad on Linkedin. I wonder how many people even noticed. I rarely pay attention to linkedin emails. On facebook it was very much noticed and I had lots of comments and questions. Most of them were good, or at least well meaning.
I agree with both comments about bravery. I get "you are so brave" comment constantly, and I understand where they are coming from because they see it as going against society. Which is a hard thing to do. I myself don't feel that way and like others did it to save my life and to be happy. A desperate, but well worth it, change.