Basically, I want to make sure I always get the computer name and not the proxy or other hardware.
No, you cannot.
Everything the server knows about the client is only done through the user agent string that the browser provides, since users can modify the user agent string and proxies can strip or modify it, you can't make any assumptions.
I don't think this is always possible. If the user is using an anonymous proxy, there really is nothing you can do.