Why Draupadi is called as Trihayani ?
त्रिहायणी – त्रयो हायना यस्याः । “दामहायनान्ताच्च ।” ४ । १ । २७ । इति ङीप् ।
The one who is present in all three Yugas
Reference in Brahma Vaivarta Purana (ब्रह्मवैवर्त पुराण)
It is mentioned in Brahma Vaivarta Purana (ब्रह्मवैवर्त पुराण) Prakrti Khanda 14.53
कृते युगे वेदवती कुशध्वजसुता शुभा।
त्रेतायां रामपत्नी सा सीतेति जनकात्मजा॥
तच्छाया द्रौपदी देवी द्वापरे द्रुपदात्मजा।
त्रिहायणीति सा प्रोक्ता विद्यमाना युगत्रये॥
In Krita (Satya) Yuga, Vedavati (वेदवती) was there as the daughter of Kushadhvaja (कुशध्वज), in Treta Yuga she became wife of Lord Rama and born as daughter of Janaka.
In Dwapara, she was born as daughter of Draupad from the fire, since she was present in all three Yugas, so she is called as Trihayani (त्रिहायणी)