It was Jayasamhita (pronounced: jaya-samhitah). Name has its root in the fact that its climax is winning of Pandavas over Kauravas. Victory is called jaya in Sanskrit. Also there is a special cryptic way to represent numbers, in Sanskrit, and in that code, jaya means 18, which is number of books (parvas) in Mahabharata. Hence this name. Its another name is also Shatasaahasri samhitaa (literally, collection of a hundred thousand verses).
As far as I can tell, there is no other name for the Mahabharat. It is a story within a story, and different scholars have varying opinions about the core story. Two of the different redactions are called Jaya and Bharata.
Mahabharat is the longest epic that describes the great war that happened some 5000 years ago in India. It has 90,000 double verses. Bhagavad Gita, the Book of Hindu dharma, is just a 700 verse chapter of Mahabharat. Gita is the short summary of the Vedas that has 20,000 verses.
It has not changed name. It is pronounced mahaa-bhaarat
Bhaarat, BTW, is the original name, still in use, of India.
Yuva and jaya are the two oldest name of Mahabharata.
The ancient name of mahabharata is Jaya
jaya samhita
Jaya Samhita
Jay Samhita
Jaysahita
The original name of the Mahabharata is Mahabharata.
Devrata or gangaputra
jayasanhita
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Jaya
Mahabharata itself. It is an epic narrative of the Kurukshetra War and the fates of the Kauravas and the Pandavas.
Dritharashtra
dhussala
Delhi
"Indraprastha" according to the Mahabharata
Arjun
Jaya