Douglas Harper's Etymology Dictionary
Bhagavad-Gita
dialogue between Krishna and Arjuna inserted in Mahabharata, from Sanskrit, "Song of the Sublime One," from Bhaga, a god of wealth, from Sanskrit bhagah, literally "allotter, distributor, master, lord," from bhajati "assigns, allots, apportions, enjoys, loves" (related to Avestan baga, Old Persian baga "master, lord, god") + gita "song," fem. past participle of gayate "sings, calls," from PIE root *gei- "to sing" (cognates: Avestan gatha "song," Lithuanian giedoti "to sing").
Wiktionary
bhagavad-gītā
n. (alternative spelling of Bhagavad-gita English) or Bhagavad Gita.