Butler Shaffer notes some corrections here to his list of pen names, but I have a few more corrections to add:
Mary Wollstonecraft (not Woolstonecraft) was Mary Shelleys mother, not her secret identity. Shelley was the daughters married name. Although her maiden name was Godwin, not Wollstonecraft, Mary Shelley went by Mary Wollstonecraft Shelley, so this may be another case of a middle-name-mistaken-for-real-last-name.
Ovid, Horace, Vergil, and Livy arent pen names, since they never called themselves by those names; those are just the English versions of their names (just as, e.g., Aristotle and Jesus are the English forms of Aristoteles and Yeshuah).
Montesquieu wasnt Charles Secondats pen name, it was his title of nobility: he was Charles Secondat, Baron de Montesquieu. (Like John Clayton, Lord Greystoke.) Ditto, mutatis mutandis, for Lord Kelvin.
(Also does a name count as a pen name if one adopts it as one’s legal name? I believe Alisa Rosenbaum legally changed her name to Ayn Rand (to protect her family in Russia).)