I know its 'technically' incorrect, but I prefer 'nollie half cab' because the nomenclature is confusing in skateboarding. A half cab is a fakie backside 180, while a nollie half cab is a nollie frontside 180 - even though in my head its the same trick, spinning in the same direction, just that the stance is different. If I'm playing a game of skate and someone says nollie frontside 180 I'd have to think about what direction they're referring to, since it would be opposite to fakie. Also, some people don't know the correct nomenclature, so they may be getting the two directions mixed up. With 'nollie half cab' everyone immediately knows the direction of rotation.
I also don't understand why a half cab or cabellarial is considered backside? In theory your chest would be facing the coping before your back would. Even if you're approaching switch stance rather than fakie, you would still be rotating a switch frontside 360...
I also like the term 'nollie cab' to describe a nollie frontside 360. its short and sweet and sounds cool.