Need advise.. Name change

So to start, I am 22 years old, live 3,000+ miles away from my entire family, and am trying to make reparations with my parents after several years of turbulence and dosconnect (on all of our parts). For a few years I did not have contact with my parents. Things are mostly fine and open between us now, except for one major detail.

When I was 17 I changed my first and middle names socially (just within my friend circle). As the years went on I began to embody this new name and when I moved across the country by myself I established myself in my new town as the name I chose at 17. So at work, in public, with all my friends, with my partner, etc, I go by the name I prefer.

The only thing is, my parents don't know about any of this. They (and my whole family) still call me by my birth name, and now that we're trying to be a family again it's very upsetting to hear this name that I associate a lot of trauma and sorrow with. It doesn't feel like me anymore and those who knew me before I changed my name have confessed that my new name suits me so much better.

How can I approach this conversation with my parents? I would like to change my name legally in the next few months as soon as I can comfortably afford to. My parents are divorced so I will have to speak to them separately. I feel like this secret I've kept for the past 5 years is starting to catch up with me and I cannot let it go any longer but I'm scared to open up to my parents this way.

Any advise would be greatly appreciated! My mom and stepdad are flying out to visit me for Christmas this year so I'd like to tell them before then.