The Shem HaMephorash, the explicit or distinguished Name, is in later Jewish mysticism a divine name of seventy-two three-letter groups, and its derivation is exact.
Exodus 14:19, 14:20 and 14:21, the verses describing the pillar of cloud moving behind Israel at the sea, each contain exactly seventy-two letters in Hebrew. Written one above another, with the first read right to left, the second left to right and the third right to left again, the three rows give seventy-two vertical columns of three letters each. Those columns are the seventy-two names.
The letter counts are checkable and correct, and the alternating reading is what makes the columns work. It is a real construction, not a vague claim.
Its age is often overstated. The Talmud knows divine names of twelve and forty-two letters, at Kiddushin 71a, but not this one. The seventy-two-part derivation is explained by Rashi in the eleventh century, appears in the Sefer HaBahir around 1150 to 1200, and is central to Sefer Raziel HaMalakh. It is therefore medieval, and describing it as ancient or Mosaic is a claim the sources do not support.
From Hebrew it passed into Latin Christian magic. Roger Bacon complains in 1260 about corrupt versions of the Liber Semamphoras circulating in the West. Johann Reuchlin, in De Arte Cabalistica of 1517, listed the seventy-two names with the suffixes -el and -yah attached, converting them into seventy-two angels, and that list, not anything Jewish, is the direct ancestor of the seventy-two angels of modern Western occultism and of the Shemhamphorash tables printed in nineteenth-century grimoires.