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Josephine is fine and so is Jo. I knew a Josephine at school who went by Jody, which is not good.
Penelope is an excellent name and all its possible nns are fine too.
Alasdair looks very distinguished: could lead to pronunciation and spelling issues, but it would be worth it!
Cato where I live wouldn't really work. It's used though rarely as a nn for Catherina and is also the name of a ghetto suburb notorious for violent rioting. If you stick to ancient Rome it'd be fine.