The Gita places this threefold formula in its seventeenth chapter as the name Brahman was given from the beginning, and states that the Vedic sacrifices, the giving of gifts and ascetic practice have always been undertaken by reciting it, which frames the phrase as older than the Gita itself even though the Gita, usually dated somewhere between the second century BCE and the second century CE, is our first attestation. Its continuing use tracks precisely what the verse claims for it, it is spoken to complete an act, appended at the close of a donation, a ritual or a vow rather than recited as a mantra of contemplation in its own right, and Hindu ritual manuals still instruct that gifts and sacrifices be sealed with it today, so the transmission has been remarkably faithful to the function the text itself describes.
Commentators split over whether om, tat and sat are three names of one reality or three names doing three different jobs. Shankara's Advaita reading treats all three as pointing at a single undifferentiated Brahman, with the grammatical distinctness of the words serving devotional completeness rather than marking real distinctions. Ramanuja's qualified non dualism reads more into the sequence, tat as the impersonal, remote designation suited to philosophical reference, and sat as being or goodness, a term that in his tradition carries ethical as well as ontological weight, so the formula moves from an abstract name toward a description of the good a personal deity actually is. Translating sat alone shows the stakes: existence, being, truth and goodness are all defensible renderings in different Sanskrit contexts, and the Gita commentators do not agree on which one is primary here.