And why should it be important, except for maybe to a few bored historians of the region? Why do we have these names?
Well, I hate to break it to you, but... as Christians we are all Jews.
You see, Christianity, much like the Bible , didn't just fall out of the sky one day in the first half of the first century. Instead it was formed as a sect of Judaism. That's right, the Blessed Mother, the Apostles, and all the other earliest Christians were all Jews. These particular Jews just happened to follow a Rabbi who happened to be the Son of God. So, if we want to be more like the first Christians -as all Christians should- we have to be more like the Jews.
On the surface, it would seem that the Protestant, particularly the non-denominational- is doing the best job of this; with their loose association to one another, their focus on preaching and reading the Scriptures as the center of the service, and what have you. But we need to go deeper.
The Protestant is very similar to the modern Jew, particularly the Reform-Jew. However, modern Judaism only exists as it does because the Temple in Jerusalem is no longer there. So, the early Christians were in no way modern Jews and were instead ancient, Temple-going Jews; so it makes sense that they formed their practices into something very similar to the Temple worship, i.e. the Church.
Early Christians had an understanding, made more concrete by the destruction of the Temple in Jerusalem, that the Church was the new Temple, with Christ as the High Priest and the Sacrificial Lamb who offers himself before God for the people. This understanding explains why Gentiles were allowed into this new and rising sect of Judaism, there was a New Israel. The members of the Church were the New Israelites, with a New Temple worship (i.e. the Mass). This New Israel prayed the Psalms, the way that the first Israelites had, they prayed to the same God, and even called him "The God of our Fathers," claiming the Jewish Patriarchs as their own spiritual ancestors. Christian communities in the time of the New Testament were remarkably Jewish, in their Worship, their Scriptures, their hymns, pretty much everything. So much so that the Roman's considered them, for some time, to be nothing more than a sect of Judaism, and they were treated the same as the other Jews by the government and citizenry.
So, back to the original question: why is the Old Testament important for Christians?
It's beyond important, it's essential, because we are the inheritors of the promises and covenants that God made with Israel. We need to know the histories, because they are OUR HISTORY. Even the apparently banal genealogy of begotten and begetting is important for us because it is the genealogy, as the Early Church Fathers tell us, of our very Salvation!
So, don't be confused by the Old Testament, and don't be ashamed of the Jewish roots of the faith. In fact, be more Jewish: respect and even fear the words of the Scripture, for they are the very Word of God, pray Evening Prayer (Vespers) on Saturday nights with the same regularity and enthusiasm that the pious Jew Prays on Friday evening, do less work on Sundays, spend more time with your family and with God, bring praying the Psalms more intimately into your spiritual life, and above all, be respectful and joyful whenever you enter The New Temple to celebrate the New Passover, with the New and Perfect Sacrifice.