You must not be pronouncing it the way I am, then. If you take the "e" out of
Emily, you have Mily, aka
Millie. I fail to see how it's a stretch. My other options are
Emilia,
Camille,
Camilla, or
Rosemary (my grandmother's legal first name was
Mary, and everyone called her Mild
Red or
Rosie because of her hair colour). I can't use
Mildred or
Millicent because my grandmother vocally hated both of those names.