I don't care for the name Elena, and I don't think nicknames should be planned by the parent(s) (before the child is even born, no less!), but left up to the child. Nonetheless, I suppose Nelly could work.
AnElena I know is often called Lainey. I'm not sure if that is how it would be spelled, but I do like the sound of it. Her name is ElenaLynne. Isn't that cheery to say?