More specifically your ISP gives you your IP address. Their Log file looks something like this (very general , NOT EXACT)

Leased IP address 204.200.156.255 to HWADDR 00:00:00:FF:FF:AB:BA


They take this, then they goto the billing department and they say "Hey who did we give cable modem 00:00:00:FF:FF:AB:BA to?" The billing guy types it in and says, "Looks like we gave that one to Jim Scheinheimer he lives at 1456 oacrest terrace se. He downloaded 15gbps of data last month, and uploaded 20gbps."




Ohh and FYI, unless you are running some type of anonymous routing or proxy system, if you are successfully downloading data off of a p2p network right now, PEOPLE CAN SEE YOUR IP ADDRESS.

Look at it sort of like a telephone. Feel free to publish a fake telephone number in the phone book or unplug your telephone from the wall, nobody can call you (aka you cannot download). But if you want to be able to recieve calls (aka download files) the sender MUST KNOW YOUR ACTUAL IP ADDRESS. The same goes with changing your telephone number. Feel free to change it every day, or even sooner. But if you want to recieve an incoming call, you must let others know your current telephone number. Unfortunately its how the internet works.