This species of banana is native to Assam, in northeast India. For many years (including when this entry was first written), the scientific name of Musa velutina was used, but Musa dasycarpa seems to have naming priority.
The long-time name of Musa velutina is the source of the common names. The USDA Plants Database uses hairy banana, but nearly every other site I found discussing this plant used a common name of pink banana. The formerly-used specific epithet velutina means “velvety”, so I find myself somewhat in agreement with the common name used by the University of Connecticut EEB Conservatory: velvet pink banana. That said, dasycarpa means “shaggy fruit”, so perhaps shaggy-fruited pink banana should be used.
The research behind restoring the older name of Musa dasycarpa was documented in this paper published after this entry was originally written: Taxonomic history and identity of Musa dasycarpa, M. velutina and M. assamica (Musaceae) in Southeast Asia (PDF).
For an extensive account of bananas, see Morton, J. 1987. Banana. p. 29–46. In: Fruits of warm climates..