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It would help if you could narrow down the ancestry. Italian names are very different from French names, etc.
If I focus on the Italian part, then:

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Father: Cesare

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If I assume they had kids in an English-speaking place, probably the U.S. I would go for simpler names that are variants of names used in Italy (I wouldn't recommend something like Gwendolyn):

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Son: Adrian (Also a Roman emperor, I guess the father would like "powerful" names like his own for a boy)
Daughter: Elena

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Mother: Caterina