If by "most correctly", you mean "the closest to what Koine Greek would do", then yes. Note however that each language will impose restrictions on the allowed sounds and sequences of; for example Finnish won't use [ä] like Ancient Greek would, simply because the sound isn't there in Finnish (it adapts it to an [ɑ]).

Also note the word itself can be pronounced multiple ways even in Koine Greek. For example the ⟨αῖ⟩ diphthong can be read as either [äɪ̯] (as in English "by") or as [ɛ:] (as in English air); as far as I'm aware this sound change happened in early Koine Greek times.

Never really understood why English insists of weirdly dropping the final bits of Greek and Latin names (“Plutarch” vs “Plutarkhos”, “Justinian” vs “Justinianus” etc)

Short explanation: English does it because it's what French does. And French does it because of its history as a Latin descendant.

Long explanation:

Since French is a Romance language, it's the result of a Latin dialect undergoing a bunch of sound changes. Those sound changes affected all words inherited from Latin. For example capus/capum¹ → chef, bonus/bonum → bon, Romanus/Romanum → Romain (yup, it applies to personal names!) ille → le, so goes on.

However, Latin is a prestige language in Europe. So even if French is a Latin descendant, it kept reborrowing words from Latin. And because of the above, French started changing those loanwords in a specific way, that kind of mimics part of its own evolution.

In other words: French developed a convention on how to handle Latin borrowings². And part of that convention is to sub/remove the endings. Other Romance languages do something similar³.

What I said applies to the Latin names. Now, the Greek names go one step deeper: Latin itself borrowed Greek words left and right, adapting them into Latin. Some would be eventually inherited by French. So the convention on how to handle Latin names in French also handles Greek names: "Latinise them first, then pretend they're Latin words."

Then you get English. Most of that Classical knowledge entered English through French, so English borrowed that convention of adapting Latin words too. Eventually developing its own convention on how to do it, that looks kind of similar to the one French used back then. And some names were subjected to local sound changes, and just like the Romance languages English messes a fair bit with word endings. And the vowels, too (Great Vowel Shift).

In contrast, German also treats Latin as a prestige language. But since it's neither a Romance language nor borrowing the convention from one, it's getting the names straight from Latin, and modifying them a bit less⁴. That includes keeping the nominative endings of the words.

NOTES:

1. I'm listing words by their Latin nominative and accusative. The nominative is the form likely to be borrowed; however, French and the other Romance languages inherited the accusative.
2. This can be seen by the Modern French renditions of those names: Ptolémée, Justinien, Plutarque.
3. For reference, look at the Italian versions of those names: Tolomeo, Giustiniano, Plutarco. Parts of the ending are still there, unlike in French, but the ending -s/-m is gone.
4. It still does change them, mind you. After a word is borrowed into a language, it's subjected to the sound changes of that language; plus spelling plays a huge role, and even in non-Romance languages there are minor conventions on how you're "supposed" to handle Latin names. Cue to German spelling "Justinianus" instead of "IVSTINIANVS" or "Iustinianus".

Sorry for the wall of text.