There is another close family connection to the name. Earl Spencer’s (Diana’s brother) 2 yr old daughter is named Charlotte Diana.
Oh that is interesting.
Earl Spencer is himself a Charles. I can imagine why someone would assume that his daughter is named after him (if not also after others, but maybe primarily after him).
Because of my interest in names, I read a number of recent news articles about the naming speculation when "Charlotte" was one of the favorites. I don't remember any mention there that "Charlotte" has either of these family connections, and I wasn't even aware of the existence of Charlotte Diana until I read this thread. Those articles were more concerned with the baby's grandfather and that Queen Charlotte.
Yet another possible family connection, not mentioned yet in this thread, is to Carole Middleton. She has a name that's more distantly related to "Charles." As others have posted here, the usual Latin form of "Charles" is "Carolus," and there are other related names, such as names in other languages and female versions. (I may also imagine someone assuming that Pippa's middle name comes from her mother's name.)