Hi APAK,
Koine Greek is very precise, so we shouldn't look at it as having the same looseness as American English. Koine Greek uses articles with all proper nouns unless there is a reason not to. Typically that reason is because both nouns refer to the same object.
The correct Koine Greek way to say that Peter is talking about 2 different objects would be to say, The God and The Savior Jesus Christ. That way know know that he's speaking of a first "the", in this case, the God, and a second "the", in that case, the savior.
But the way this is written is The God and Savior Jesus Christ. So "the" is applied to both nouns as the same object.
Another example would be in Titus:
View attachment 11617
When you look at the syntax of each word in this clause, well, that's how we identify the clause is by the common syntax.
Here we have a shared article introducing the Genetive case answer to the previous clause, "the happy expectation and appearance of the glory". Paul writes of the about our happy expectation, even the appearance of the glory of, whom?
The appearance of the glory of the ____________________. And what comes after this article, sheltering under it's umbrella, if you will, is part of the same. In this case, "Our God and Savior Jesus Christ".
We see the same construction in the preceding clause itself, the happy expectation IS the appearance of His glory.
The fact that 'Savior' does not have an article, this is to point us back the preceding article, and joins the object to the object of that article.
Forgive my verbosity, I feel like I should be able to explain this more simply, but Greek class was a lot of years ago!
Much love!