In this video, Charles Willemen seems to suggest that the group which split off and went south, and came to be identified as Hinayana, originally referred to itself as Mahayana.
It seems that, in those very early days, there weren't the same sharp sectarian divisions that came later:https://en.wikipedia.org/wiki/Hinayana
I realize that, as Pure Land Buddhists, we're not followers of the Dalai Lama, but I find him a worthwhile source when it comes to the history of Buddhism:
It is very important to understand that the core teachings of the Theravada tradition embodied in the Pali scriptures are the foundation of the Buddha's teachings. Beginning with these teachings, one can then draw on the insights contained in the detailed explanations of the Sanskrit Mahayana tradition. Finally, integrating techniques and perspectives from the Vajrayana texts can further enhance one's understanding. But without a foundation in the core teachings embodied in the Pali tradition, simply proclaiming oneself a follower of the Mahayana is meaningless.
If one has this kind of deeper understanding of various scriptures and their interpretation, one is spared from harboring mis-taken notions of conflicts between the "Greater" versus the "Lesser" Vehicle (Hinayana). Sometimes there is a regrettable tendency on the part of certain followers of the Mahayana to disparage the teachings of the Theravada, claiming that they are the teachings of the Lesser Vehicle, and thereby not suited to one's own personal practice. Similarly, on the part of followers of the Pali tradition, there is sometimes a tendency to reject the validity of the Mahayana teachings, claiming they are not actually the Buddha's teachings.
As we move into our examination of the Heart Sutra, what is important is to understand deeply how these traditions complement each other and to see how, at the individual level, each of us can integrate all these core teachings into our personal practice."http://viewonbuddhism.org/vehicles.html#3