There are two options for this:
1. Change your name on your primary profile, don't be ashamed of it, and don't worry about it. This is the method that I chose. I decided that I didn't want to even give people the option of clinging to the male me and pretending that the female me didn't exist. They could either accept me as I am, or not at all. I first posted a coming-out letter, along with changing the gender marker on my profile, and then once I went full-time, I changed the name too. I know this isn't possible for everyone, but it ended up working perfectly in my case. I didn't lose any friends that I'm aware of. And if I did, that's their problem. And now I can unashamedly be myself, and all those years where I was ashamed of hiding, ashamed of being seen as by a weirdo by my friends, in a way I feel vindicated.
2. Start a new profile under a new name, come out on your old profile and invite those who wish to friend the new you to come over on to your new profile and do so, while leaving the old profile up as an inactive relic. This option minimizes the damage. People who aren't okay with it can just stay on your old profile and not friend you on your new one. Also if you need to, it can give you a separate profile to express yourself freely on without the stigma of being watched by your friends if you're not ready to come out publicly yet.