I think you can pretty much make a nickname out of every name. My mom chose
Leah for me thinking it would have no nicknames. When I was about 10 a next door neighbor teen referred to me as
Lee Lee.
Eden is not the best choice for no nicknames because its obvious she may be called
Edie.
I would go with something like
Sarah. I mean, I have heard people use
Sadie for a nickname, but its not intuitive.