A 1/30th scale model would still be over 30 feet tall. (The real tower is nearly 1000 feet/300 meters tall.) Are you sure you don't mean, say, 1/300th scale?

My friends all call it The Claw :P

There are some people who call it the Space Claw: https://www.flickr.com/people/spaceclaw

I've heard it referred to as the box that the Transamerica Pyramid came in (both were built at around the same time).