Whether or not you guessed Elizabeth, the current queen of England, pick a couple of new names for the youngster. One fitting for a princess and one where her future isn't already planned out.
Elizabeth is a great name, I think, for a Princess or not. Bess would be an adorable nickname for the little one, or Betty. Were I to rename her I might go with Alice Ann, or for a princess, Katherine Cecilia Amandine Georgette.