My mom actually did a very similar thing. Her birth name was Jean Anne, which she hated, so she has been calling herself GiGi since high school and had it legally changed at 18. My name is Megan Elizabeth, which my mom named me hoping I would go by the nickname "Meliz".

Unfortunately I'm not as cool as her, and went by Megan through high school. When I was 16, a teacher just started calling me "Meg", and I never corrected her because I liked it. When I went to college I just introduced myself as Meg and have continued to do so in my professional life. You can actually tell who has known me before I was 16 because they will still sometimes call me Megan, where as people I met later on only ever call me Meg.

That's kind of the one piece of advice Id give to OP. Be kind to those who knew you as Megan and got used to calling you that. If you're less militant about it you'll probably get way less pushback from these people. I let my family and old friends call me Megan (although they do call me Meg at least half the time), and if a new person hears that and asks, I just tell them I prefer Meg.

I had a friend in college who we all met as "Chrissy" but wanted to change that to "Christine" junior year, but she was very pushy and confrontational about it, which made us less likely to call her Christine. It was jerky of us, but it did happen.