Jerusalem is mentioned many hundreds of times in the Jewish Bible. As for the Chumash (Five Books of Moses), it is true that the word "Jerusalem" does not appear there. Most simply, this is because it was not yet called Jerusalem.
Under Jebusite rule and earlier, Jerusalem was divided into two cities, the western part called Jeru (Yere) and the eastern part called Salem (Shalem). Both of these names do appear in the Five Books: "And Malki-Tzedek, King of Shalem" (Gen. 14:18). "And Abraham called that place...Yere" (Gen. 21:14).
Around the time of Joshua's conquest, the Amorites consolidated the two halves of the city, and they combined the two names: Jeru-salem. From this point on in history, our Bible refers to Jerusalem countless times.
Furthermore, the Chumash refers 19 times to "the place that God will choose" as the center for Jewish life and religion (e.g. Deut. 12:11, 14, etc.) The Prophets Samuel and Gad finally reveal to King David that this chosen place is Jerusalem and the Temple Mount.
So here's another reason Jerusalem isn't mentioned explicitly in the Chumash as the holy city: It hadn't yet been revealed as such. Maimonides, writing around 800 years ago, offers three reasons that the Chumash does not reveal the identity of the holy city:
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If the nations had learned that this place would express the highest Jewish ideals, they would have united in an effort to occupy and prevent the Jews from ever controlling it. (Sound familiar?)
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If they had known of Jerusalem's spiritual stature, they may have tried to take advantage of its spiritual nature by making it into a center of idol worship.
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Each of the twelve tribes would have desired to have Jerusalem in their borders, and this would lead to disunity.
Once the Jewish nation had conquered and divided the land, the above ceased to be considerations.
So, in conclusion, Jerusalem with its name has played a prominent part in Jewish history and writings for thousands of years.
