As for that signature—Elizabeth R—the R stands for Regina, which means “queen.” Regina is not actually part of the queen’s given name. She was baptized as Elizabeth Alexandra Mary Windsor
She could have taken another name when she was coronated but she chose to stick with Elizabeth. Not a bad choice. Once crowned, I believe she was no longer Elizabeth Alexandra Mary Windsor, but simply HRH Elizabeth II, Regina. If she were a man it would be Rex instead of Regina.