XP has two names, the original one, and the "visual" one that is shows you.
But that may not be your issue. You said the name conflics with another on the network? I think that is refering to computer name, not user name. If I'm not mistaken, multiple computers can have the same user name, but not the same computer name.
Anyways, to check computer name, right click My Computer and choose Properties. Look under the Computer Name tab and see what it says in there. "Full computer name" is what I'm thinking about.
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But as for the name. Well you could be talking about "registered owner" name. Which is different from login name.
But anyways, I think I see what you're getting at. And I'm not to sure you CAN change that name. Only because XP has your entire profile and registry entries under that name. As well as security certificates and file encryption (if used) and uses it to encrypt your profile directory for privacy (if on). So it's not easy to change.
Try going into Start-Run and type "control userpasswords2". A box should pop up with any users you have. Click yours and then Properties. It should show you some various things. Not sure if you can actually "change" your name from here though.