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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.
Going to throw in a few other unique examples like how Alexandria Ocasio-Cortez is almost always called by her first and last name or the initials AOC. Similarly Ilhan Omar is almost always referred to by her first and last name.
The right loved to call Obama, Barack Hussein Obama with emphasis on Hussein to highlight how non-white he was, pin him as Muslim, and draw associations to Sadam Hussein. This was done to rile up their xenophobic and racist base.