Of the many epithets used to describe Dionysus in Orphic Hymn XXIX, thrice begotten ("τρίγονον" in the original) stands out:
Bacchus I call, loud-sounding and divine,
Fanatic God, a two-fold shape is thine:
Thy various names and attributes I sing,
O, first-born, thrice begotten, Bacchic king:
Rural, ineffable, two-form'd, obscure,
Two-horn'd, with ivy crown'd, euion, pure.
Bull-fac'd, and martial, bearer of the vine,
Endu'd with counsel prudent and divine:
Triennial, whom the leaves of vines adorn,
Of Jove and Proserpine, occultly born.
Immortal dæmon, hear my suppliant voice,
Give me in blameless plenty to rejoice;
And listen gracious to my mystic pray'r,
Surrounded with thy choir of nurses fair.
The Hymns of Orpheus, Translated by Thomas Taylor
Dionysus is a dying-and-rising god, I could understand being called twice-born. But thrice-born? What is the story here?