Contemporary USGS maps name this gulch, and the beach just north of it, Li`i lioholo, which means "little running horse" in Hawaiian. However, earlier sources give the name of the beach as `Ili`iliholo:
When the sand disappears from the beach at Kama`ole II, a large bed of shingle is exposed, and as the waves surge and recede across these rounded beach rocks, or `ili`ili, an ominous rumbling results. The Hawaiians called this beach `Ili`iliholo, "running pebbles", for this unpredictable and dramatic phenomenon.
—from The Beaches of Maui County by John R. K. Clark, 1980.
The 1929 Walter E. Wall Map of Maui spells the name `Ili`ilioholo.This gulch runs from 5000 feet at the edge of the Kula Forest Reserve northwest to the boundary between Kama`ole Beach Parks II and III, and is called an "intermittent stream".
Thanks to Forest Starr for uncovering these sources on the name.