Elizabeth is the great grandmother’s name but also the Kate’s mother’s name. So it is a two-fer. So is Charlotte. In fact, Charlotte is a three-fer. There is George III’s wife as you mentioned. It is Pippa, Kate’s sister’s middle name. And it is the feminine of Charles. Diana stands alone and I am very glad they picked it.
I thought about the feminine of Charles, and then forgot :-/ now that you mention it, I always figured he was named for Charles I/II, the kings associated with the Restoration, but now I wonder if perhaps he wasn’t named for his however-many-greats grandmother.