How can I get people to call me by a new nickname? Margaret -> Etta/Greta

My name is Margaret. I've never really liked it, so I want to start using a nickname. The problem is, everyone I know calls me Margaret, and I don't know how to ask them to change that. My older sisters call me Meg or Meggie sometimes, but those seem childish to me. I'm going into high school next year; I'll be meeting new people and teachers who don't already know me, so I could just introduce myself as something new. However, many of my friends will be there too, and I think it would be weird to ask them to suddenly call me something different. I don't like many of the conventional nicknames for Margaret, like Maggie, Peggy, or Marge. Greta and Etta aren't as common, but I think they're beautiful and still work. Any advice for asking friends, family, and new people to call me something new?