The public IP address is shown at sites like:
http://whatismyipaddress.com
It can be easily forced to change on Asymmetric Digital Subscriber Line (ADSL) or Fiber To The Home (FTTH) just applying the settings at the router control web site:
http://192.168.1.1
or turning off/on the router or resetting the router.
The problem arises with coaxial cable (Data Over Cable Service Interface Specification; DOCSIS) or coaxial-cable-fiber (Hybrid Fibre-Coaxial; HFC), in which case only the ISP can easily change such IP. In such cases it is possible for the user to change the public IP address, but it requires to transform the router-cable into a router-modem (which can connect a single Mac) and then add a neutral router (to have more than one Mac on the network, or a Mac and ethernet printer, etc).