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.