Change Hostname in Windows 7

The hostname and the computer name are the same. You change it by right clicking on Computer on the Start Menu, selecting Properties, pressing Advanced System Settings on the left, selecting the Computer Name tab, pressing Change..., entering your new name, and rebooting the machine when asked.

There is a difference between what a computer "thinks" its name is, and what the outside world "thinks" its name is. On the PC itself, you can only change its internal idea of its host name. In some environments, this changes the outside representation too (if Dynamic DNS is set up). However, in most cases you need to ask your network administrator to change the host name, because it is set in your network's DNS server.

So, the proper answer is, "it depends". You need to elaborate more about your environment. Is it a domain network? Home PC? NAT in effect, etc...