[thaumasiotes]

You appear to be focused on proper nouns. There's a very simple rule for them: some of them are arthrous, and the rest aren't. This question makes as much sense as asking for a rule governing when a noun should begin with B: box, book, and boat do, but knife, mail, and ghost don't. How do you tell?

There are several rules determining whether an ordinary noun should or shouldn't be marked by "the", but none of those apply to proper nouns. Those are names; they either include an article, or they don't.