"So it's purely my IP which wouldn't change?"
Your private IP would change (192.168.x.x) but not your public IP (188.8.131.52). Your public IP is what people see when you go to their website.
"I'm inquiring specifically because this suggests that my router assigns me an IP address?"
Assuming your router uses NAT, then yes. It would have a DHCP server that hands out private IP's from a certain pool(192.168.1.2-192.168.1.100). Each IP is assigned to a certain MAC address for a certain amount of time.
"they identify you that way via MAC and IP address"
Is that network on the "intranet"? Like do you need a VPN to access it? Or is it a public website you are signing into? Another words, can you access their network from ANY computer on ANY network?
What is the general problem you are trying to solve? Do they limit bandwidth per user? Do they not allow user to add their own routers and you are trying to get around that? I am open to helping no matter what, I just need to know what I am helping with.
Edited by Trikein, 28 July 2016 - 03:57 PM.