The Name of seventy-two, Shem ben Ayin Bet, is not read anywhere in one piece in the Torah. It is drawn from three consecutive verses in the story of the sea, Exodus 14:19 to 21: the angel of G-d moves behind the camp of Israel; the cloud comes between the camp of Egypt and the camp of Israel all night; Moses stretches his hand over the sea and the Lord splits it with a strong east wind. Sefer HaBahir notes that each of these verses counts seventy-two letters, and the count is exact.
The Bahir also gives the rule. The letters of the first verse, "Vayissa," are arranged in order; those of the second, "Vayavo," backwards; those of the third, "Vayet," in order again. One letter is taken from each: every name has three letters, and seventy-two names result. Rashi, on Sukkah 45a, works out the first: the Vav of "vayissa," the Heh that ends the second verse, the Vav of "vayet." That gives והו.
Why does Rashi speak of it? The Mishnah (Sukkah 4:5) describes the procession around the altar during Sukkot. Each day they said "Ana Hashem, hoshia na," "please, Lord, save now"; Rabbi Yehudah reports another formula: "Ani vaho, hoshia na." Rashi explains that אני והו has the same numerical value as אנא ה', and that these are two of the seventy-two names: והו is the first, אני the thirty-seventh. According to Rashi, then, these names belong to a supplication said in the Temple.
The Pardes Rimonim of Moshe Cordovero (gate 21, chapter 5) gives the complete list and quotes the Zohar (Beshalach 51b): the first letters go straight because they belong to Chesed; the second go backwards because they belong to Gevurah and reveal the judgments of the left side; the third go in order to show the king crowned on both sides. Cordovero links the whole to Chesed, whose value is seventy-two, and notes that the 216 letters equal Gevurah. The Bahir, for its part, compares the 72 names to the twelve stones engraved with the names of the tribes, six names on each stone.
Rabbi Nechunya ben HaKanah, quoted by the Pardes, calls these names "bridges": seventy-two crossings over the waters of Chesed. That is the register in which the tradition keeps them, the register of prayer and meditation. Sha'arei Tziyon (Prague, 1662) pairs each with a verse of Psalms in a prayer attributed to the Ari, and asks that the names be kept in thought, without being uttered. You will find here no talisman and no letter "scanning" in the manner of New Age websites: nothing of the kind is in the sources you have just read.
