Updated August 7, 2023
The name refers to the major interchange just northwest of downtown Las Vegas where I-515, I-15, US 93, and US 95 all merge, then branch out again their respective directions. The tangled confluence of highways, with all their entrance and exit ramps ("spaghetti") in one centralized junction ("bowl") account for the name.
Spaghetti Bowls aren't uncommon in cities around the country; the nearest is the one in Reno, in fact. But the more common designation is Spaghetti Junction.