The first known division of the two biblical Testaments was by a theologian and pastor in the late 2nd century, named Melito of Sardis. Melito listed 38 of the same 39 books we have today, with the only exception being the book of Esther, which he may have counted as part of one of the other books he listed.
At any rate, Melito didn’t call the Old Testament the Old Testament… Instead, he called it the “παλαια διαθήκη,” which is Greek for Old Covenant or Old Testament. But Greek is a precise language, and there are at least two words which might be translated as covenant. One is “διαθήκη” and the other is “συνθήκη.”
Unless you’re interested in studying Greek, knowing or remembering these words isn’t that important, but the distinction between the two is important.
συνθήκη means something like contract or agreement, allowing for and even expecting equality among the participants.
διαθήκη conveys the idea of a final will or testament, emphasizing a unilateral or lop-sided contract, where there’s a great benefactor and a lesser beneficiary.
We know what a final will and testament is because many of us have had to deal with settling the estate of a deceased loved one. When the deceased leaves a will behind, it’s usually far easier to distribute his or her assets according to his or her wishes, which should be outlined in the will.
The will is a formal contract, but there is obviously one party whose doing all the giving and the others are simply the beneficiaries.
The concept of a final will and testament, then, conveys what seems to be the biblical reality of God’s covenant with man – God is infinitely greater, He’s the ultimate giver, and man is merely the beneficiary. And that’s why Melito wasn’t alone in noticing that the word testament (διαθήκη) fits the biblical relationship between God and man slightly better than the word covenant (συνθήκη).
About 500 years before Melito, and almost 300 years before the birth of Jesus, 70 translators got together to translate the Hebrew Scriptures into Greek (this is called the Septuagint), and they too used the word διαθήκη to translate the Hebrew word for covenant because they also knew that God and man are not equal parties.
And around 400 AD, Jerome’s Latin translation of the Old and New Testaments (called the Latin Vulgate), followed the lead of those Greek translators. Jerome called the Old Testament the Vetus Testamentum.
Of course, all English translations have followed the Greek and Latin titles, and that’s why we call them the Old and New Testaments today, and not the Old and New Covenants, even though the English translations most frequently use the word covenant in the Scripture text itself.
The division of the Bible into the Old and New Testaments is evidence that God is a covenant-making and covenant-keeping God. A good question for the reader to ask is, “Which biblical covenant pertains to me?” I recommend that you read Hebrews chapter 9 in the Bible, and then talk about it over lunch or coffee with a good pastor or knowledgeable Christian friend.
 See Eusebius’s account of Melito’s list in point #14 of this article. Also, note that Nehemiah was counted along with Ezra (aka “Esdras”) and Lamentations was counted along with Jeremiah. https://www.ccel.org/ccel/schaff/npnf201.iii.ix.xxvi.html#fnf_iii.ix.xxvi-p59.2