Can I be a teenager for a second and say "eww" to both
Miley and
Milly!
Mila is gorgeous! Very Slavic and pretty, and the meaning is just so sweet. I pron. it MILL uh. It's already a short name, and I don't see why people would feel the need to further shorten it to something awful like
Milly. If they do, then I would just firmly tell them her name is
Mila.