If someone wants to call me Becky I will let them although it is more common to call me Becca. I like Becca better than Becky but at the same time I think of a chicken saying,"Bek-ah!" So, Rebecca is probably the best name to say. I had some friends call me Reba for the longest while and it irritated me beyond belief.
Batman do you get this all the time when meeting new people? "What do you like to be called, Becca, Becky or Rebecca?" I usually just say,"whatever you want," although as a teen I only wanted to be called Beck or Becca. That's changed now I can say....oh man, this name is more complicated than I originally thought!