you're kind of confused.

There are two basic types of address, IP and MAC. Both of these are independent from your computer. MAC address are assigned by the manufacturer to the NIC (network interface card), and cannot be changed. These are actually burned onto a ROM chip on the network card. The IP address is a layer 3 address, that has the ability to be changed. Computers usually have two IP address though, an internal, for use on the local lan, usually a class C with a 192.168.0.xxx, and an external address, used to view your computer from the 'internet'. The internal address can be whatever you want, but the external is supplied by your ISP. HTRegz gave some good links and tips as too how this works.