How do I register a UCLA Domain Name?

My department chair asked me to come up with a short, catchy, stand-out domain name, how do I know whether I can do this and, if so, how do I go about registering it? 
 UCLA Policy 411 deals with the registration and use of UCLA domain names and can be found at: UCLA Policy 411 – 	Registration and Use of UCLA Domain Names 
 Once you understand the policies that pertain to your request, the next step is to follow the steps detailed here: 
 https://www.it.ucla.edu/services/networks-connectivity/domain-name-system