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You can change the Long User Name and the Computer name without any problems. Changing your Short User Name is a bit more tricky, and not recommended.

To change your Long User Name (in Panther), go to the Accounts Preference Pane (launch System Preferences). Click on your account in the left pane and change your Long User Name on the right. You will notice that your Short User Name is not editable.

To change the Computer Name, open the Sharing Preference Pane. At the top, you will see the option to change the name.
 
Short name change

Your short name is used as your user name. This harkens back to the unix roots. In order to change this you would need to create a new account, go through the trouble of exporting everything to that account. You would have to do that as root or you won't have access to it. It'd a pretty big pain in the .... well thats the only way I know to do that.
 
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