The ISP assign IP address to us through DHCP. Each time when you connect to Internet the DHCP server will try to find a spare IP address and assign to you. Of course the server try to assign you the last address you used before first (if available at that moment.) To anwer you question our IP address will change and depends on how you use Internet. If you keep your PC or broandband router on all the time your IP address won't change maybe for a few months. But if you are just an infrequent user you will find you may have different IP address each time.
Also in you case I believe you are using broandband router to connect to HGC service directly. You can logon to your brandband router to find out the IP address. The 192.168.0.x address is assigned by your broandband router to your PC which is private to you local LAN not Internet. Your broadband router will translate that address to ISP assign address when you get into Internet.
I think HGC's DHCP server will keep track of which IP assign to which MAC address at given time. So they are able to traceback who has been using the IP even through we don't need to logon ISP for connectivity each time.