I think people tend to choose the more unique/recognizable name to call candidates by. For example, we also call Bernie Sanders by his first name more often than his last. “Harris” is a more common name than “Kamala”. “Clinton” could be confused for Bill, but “Hillary” isn’t going to be mistaken. I don’t think it has anything to do with the candidate’s gender.
Not the person you replied to, but just wanted to say thank you for taking the time to write up such an informative answer. I learned quite a few things from it.