I'll offer a partial/praeliminary answer. I don't know about those Biblical names—that is, I don't know how they are declined, because they're from Hebrew.
There are two situations that spring to mind:
In classical Greek, I believe the adjective is generally preferred, if one is available. So you would rather say Ἀθηναγόρας ὁ Ἀθηναῖος, "Athenagoras the Athenian".
In that case, the adjective needs to agree with the head of the noun group, the noun Ἀθηναγόρας. Since Ἀθηναγόρας is in the nominative case, it probably being subject or subject complement in the sentence, both the article ὁ and the adjective Ἀθηναῖος are also in the nominative. Had it been an object Ἀθηναγόραν, as in "she saw Athenagoras the Athenian", the whole would be in the accusative case: Ἀθηναγόραν τὸν Ἀθηναῖον. The same applies mutatis mutandis to a possible genitive or dative.
If no adjective is available, or the second construction is chosen for some other reason, of Athens is not adjectival, but it is its own noun with article. Then you would not use the adjective, but you would use whatever the relevant noun is of the town. By the translation of, you can see that both Athens and the article must then be in the genitive case. The head noun Athenagoras keeps whatever case is warranted by its function in the sentence: if it's subject, it is a nominative; if it is I gave a present to Athenagoras of Athens, then to Athenagoras would be a dative; while of Athens remains a genitive in both cases.
It is possible in either case to omit the article where there is some specific reason for brevity, or when it is used attributively, as in "the Athenian Platonists are rubbish", or for other reasons that I'd have to think about. An example is the beginning of the History of Thucydides, Θουκυδίδης Ἀθηναῖος.
When you translate any such phrase into Latin, like Athenagoras Atheniensis, of course the article disappears, since Latin has no articles.
A third option is perhaps Athenagoras, he of Athens, but then I would expect two articles between the nouns. I'm not sure whether this construction even exists.