A useful way to locate this system is to list the places it is absent from.
The seventy-two angels are not in the Hebrew Bible. No text of it names them, individually or as a group, and Exodus 14 gives no indication that its letters are to be counted.
They are not in the Talmud. The Talmudic discussion of extended divine names concerns twelve and forty-two letters. The seventy-two-letter name is not part of it.
They are not in the standard Jewish liturgy. Neither the daily nor the festival services address them, and mainstream Jewish practice has no place for a directory of seventy-two named angels with individual offices.
They are not in the New Testament, and not in the patristic angelologies, which work with the Dionysian choirs rather than with named individuals.
They are not in the Qur'an or in the Islamic angelological tradition.
Where they are is a specific and traceable body of literature: the derivation in Rashi and in the medieval Kabbalistic texts; the angelic reading in Reuchlin and the Christian Kabbalists of the sixteenth century; the systematisation in Agrippa and his successors; the tabulation with offices and verses in Lenain and nineteenth-century French occultism; the correspondences in the Golden Dawn; and the popular angelology of the last several decades.
That is a real tradition with named participants and datable stages, and it is more interesting described accurately than inflated. The frequent claim that these are the seventy-two angels of Jewish tradition, or of the Bible, is not supportable, and the tradition they do belong to is substantial enough not to need the borrowed authority.