I feel I should point out that every computer, phone, iPad, and device in my house connects to the internet via the same IP address. When we visit a web server, all these different devices will use one and the same identical IP address at any given time. Note that this IP address changes periodically thanks to my ISP doing weird network stuff. To any web servers we may visit, this public IP address is the best way to locate us.
You can easily find out what your public ip address is by visiting http://ipchicken.com/
If you are interested in knowing more about your visitors, the name of their computer is not especially helpful at all. You'd probably find more interesting information in $_SERVER["HTTP_USER_AGENT"] which will probably tell you what kind of device they are using, what OS, and possibly other things (or whether they are a the GoogleBot). If you want to track some user's behavior, send them a unique cookie and track what they do on your site. As long as they don't remove that cookie, you should be able to connect their various actions and behaviors together.
Google Analytics is a very handy tool for better understanding how users interact with your site.